Ising model - Revision history

Carl McBride: /* References */ Added a recent publication

2016-03-11T12:10:29Z

References: Added a recent publication

← Older revision		Revision as of 14:10, 11 March 2016
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	==References==		==References==
	<references/>		<references/>
			;Related reading
			*[http://dx.doi.org/10.1126/science.aab3326 Gemma De las Cuevas, and Toby S. Cubitt "Simple universal models capture all classical spin physics", Science '''351''' pp. 1180-1183 (2016)]

	==External links==		==External links==
	*[http://dx.doi.org/10.4249/scholarpedia.10313 Barry McCoy "Ising model: exact results", Scholarpedia, 5(7):10313 (2010)]		*[http://dx.doi.org/10.4249/scholarpedia.10313 Barry McCoy "Ising model: exact results", Scholarpedia, 5(7):10313 (2010)]
	[[Category: Models]]		[[Category: Models]]

Carl McBride: /* 3-dimensional Ising model */ created an internal link

2016-02-02T12:33:35Z

3-dimensional Ising model: created an internal link

← Older revision		Revision as of 14:33, 2 February 2016
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	<ref>[http://www.sandia.gov/LabNews/LN04-21-00/sorin_story.html Three-dimensional proof for Ising model impossible, Sandia researcher claims to have shown]</ref>		<ref>[http://www.sandia.gov/LabNews/LN04-21-00/sorin_story.html Three-dimensional proof for Ising model impossible, Sandia researcher claims to have shown]</ref>
	<ref>[http://dx.doi.org/10.1145/335305.335316 Sorin Istrail "Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces", Proceedings of the thirty-second annual ACM symposium on Theory of computing pp. 87-96 (2000)]</ref>		<ref>[http://dx.doi.org/10.1145/335305.335316 Sorin Istrail "Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces", Proceedings of the thirty-second annual ACM symposium on Theory of computing pp. 87-96 (2000)]</ref>
	In three dimensions, the critical exponents are not known exactly. However, [[Monte Carlo \| Monte Carlo simulations]], [[renormalisation group]] analysis and [[conformal bootstrap \| conformal bootstrap techniques]] provide accurate estimates <ref name="Campostrini2002">[http://dx.doi.org/10.1103/PhysRevE.65.066127 Massimo Campostrini, Andrea Pelissetto, Paolo Rossi, and Ettore Vicari "25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice", Physical Review E '''65''' 066127 (2002)]</ref>:		In three dimensions, the [[critical exponents]] are not known exactly. However, [[Monte Carlo \| Monte Carlo simulations]], [[renormalisation group]] analysis and [[conformal bootstrap \| conformal bootstrap techniques]] provide accurate estimates <ref name="Campostrini2002">[http://dx.doi.org/10.1103/PhysRevE.65.066127 Massimo Campostrini, Andrea Pelissetto, Paolo Rossi, and Ettore Vicari "25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice", Physical Review E '''65''' 066127 (2002)]</ref>:

	:<math>		:<math>

Carl McBride: /* 3-dimensional Ising model */ Added a "red" link to conformal bootstrap

2016-02-02T12:31:12Z

3-dimensional Ising model: Added a "red" link to conformal bootstrap

← Older revision		Revision as of 14:31, 2 February 2016
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	<ref>[http://www.sandia.gov/LabNews/LN04-21-00/sorin_story.html Three-dimensional proof for Ising model impossible, Sandia researcher claims to have shown]</ref>		<ref>[http://www.sandia.gov/LabNews/LN04-21-00/sorin_story.html Three-dimensional proof for Ising model impossible, Sandia researcher claims to have shown]</ref>
	<ref>[http://dx.doi.org/10.1145/335305.335316 Sorin Istrail "Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces", Proceedings of the thirty-second annual ACM symposium on Theory of computing pp. 87-96 (2000)]</ref>		<ref>[http://dx.doi.org/10.1145/335305.335316 Sorin Istrail "Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces", Proceedings of the thirty-second annual ACM symposium on Theory of computing pp. 87-96 (2000)]</ref>
	In three dimensions, the critical exponents are not known exactly. However, [[Monte Carlo \| Monte Carlo simulations]] ~~and~~ [[~~Renormalisation~~ group]] analysis provide accurate estimates <ref name="Campostrini2002">[http://dx.doi.org/10.1103/PhysRevE.65.066127 Massimo Campostrini, Andrea Pelissetto, Paolo Rossi, and Ettore Vicari "25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice", Physical Review E '''65''' 066127 (2002)]</ref>:		In three dimensions, the critical exponents are not known exactly. However, [[Monte Carlo \| Monte Carlo simulations]], [[renormalisation group]] analysis and [[conformal bootstrap \| conformal bootstrap techniques]] provide accurate estimates <ref name="Campostrini2002">[http://dx.doi.org/10.1103/PhysRevE.65.066127 Massimo Campostrini, Andrea Pelissetto, Paolo Rossi, and Ettore Vicari "25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice", Physical Review E '''65''' 066127 (2002)]</ref>:

	:<math>		:<math>

Carl McBride: /* 3-dimensional Ising model */ Cited a newer reference

2011-07-26T10:30:48Z

3-dimensional Ising model: Cited a newer reference

← Older revision		Revision as of 12:30, 26 July 2011
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	<ref>[http://www.sandia.gov/LabNews/LN04-21-00/sorin_story.html Three-dimensional proof for Ising model impossible, Sandia researcher claims to have shown]</ref>		<ref>[http://www.sandia.gov/LabNews/LN04-21-00/sorin_story.html Three-dimensional proof for Ising model impossible, Sandia researcher claims to have shown]</ref>
	<ref>[http://dx.doi.org/10.1145/335305.335316 Sorin Istrail "Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces", Proceedings of the thirty-second annual ACM symposium on Theory of computing pp. 87-96 (2000)]</ref>		<ref>[http://dx.doi.org/10.1145/335305.335316 Sorin Istrail "Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces", Proceedings of the thirty-second annual ACM symposium on Theory of computing pp. 87-96 (2000)]</ref>
	In three dimensions, the critical exponents are not known exactly. However, [[Monte Carlo \| Monte Carlo simulations]] and [[Renormalisation group]] analysis provide accurate estimates:		In three dimensions, the critical exponents are not known exactly. However, [[Monte Carlo \| Monte Carlo simulations]] and [[Renormalisation group]] analysis provide accurate estimates <ref name="Campostrini2002">[http://dx.doi.org/10.1103/PhysRevE.65.066127 Massimo Campostrini, Andrea Pelissetto, Paolo Rossi, and Ettore Vicari "25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice", Physical Review E '''65''' 066127 (2002)]</ref>:

	:<math>		:<math>
	\nu=0.~~6298~~ (5)		\nu=0.63012(16)
	</math><ref name="Hasenbusch">[http://dx.doi.org/10.1103/PhysRevB.59.11471 M. Hasenbusch, K. Pinn and S. Vinti "Critical exponents of the three-dimensional Ising universality class from finite-size scaling with standard and improved actions", Physical Review B '''59''' pp. 11471-11483 (1999)]</ref>		</math>

	:<math>		:<math>
	\alpha=0.~~108~~(5)		\alpha=0.1096(5)
	</math> <ref name="Kolesik"> [http://dx.doi.org/10.1016/0378-4371(94)00302-A Miroslav Kolesik and Masuo Suzuki "Accurate estimates of 3D Ising critical exponents using the coherent-anomaly method", Physica A: Statistical and Theoretical Physics '''215''' pp. 138-151 (1995)]</ref>		</math>

	:<math>		:<math>
	\beta= 0.~~3269~~(6)		\beta= 0.32653(10)
	</math> <ref name="Talapov">[http://dx.doi.org/10.1088/0305-4470/29/17/042 A. L. Talapov and H. W. J Blöte "The magnetization of the 3D Ising model", Journal of Physics A: Mathematical and General '''29''' pp. 5727-5733 (1996)]</ref>		</math>

	:<math>		:<math>
	\gamma=1.~~237~~(4)		\gamma=1.2373(2)
	</math~~><ref name="Kolesik"> </ref~~>		</math>

	:<math>		:<math>
	\delta=4.77(5)		\delta=4.7893(8)
	</math~~><ref name="Kolesik"> </ref~~>		</math>

	:<math>		:<math>
	\eta =0.~~0366~~(8)		\eta =0.03639(15)
	</math~~><ref name="Hasenbusch"> </ref~~>		</math>

	with a critical temperature of <math>k_BT_c = 4.51152786~S </math><ref ~~name=~~"~~Talapov~~"> </ref>.		with a critical temperature of <math>k_BT_c = 4.51152786~S </math><ref>[http://dx.doi.org/10.1088/0305-4470/29/17/042 A. L. Talapov and H. W. J Blöte "The magnetization of the 3D Ising model", Journal of Physics A: Mathematical and General '''29''' pp. 5727-5733 (1996)]</ref>

	==ANNNI model==		==ANNNI model==

Carl McBride: /* 3-dimensional Ising model */ rearranged expression for T_c

2011-07-26T10:16:56Z

3-dimensional Ising model: rearranged expression for T_c

← Older revision		Revision as of 12:16, 26 July 2011
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	</math><ref name="Hasenbusch"> </ref>		</math><ref name="Hasenbusch"> </ref>

	with a critical temperature of <math>~~K_c = J/~~k_BT_c = 0.~~2216544~~</math><ref name="Talapov"> </ref>.		with a critical temperature of <math>k_BT_c = 4.51152786~S </math><ref name="Talapov"> </ref>.

	==ANNNI model==		==ANNNI model==
	The '''axial next-nearest neighbour Ising''' (ANNNI) model <ref>[http://dx.doi.org/10.1016/0370-1573(88)90140-8 Walter Selke "The ANNNI model — Theoretical analysis and experimental application", Physics Reports '''170''' pp. 213-264 (1988)]</ref> is used to study spatially modulated structures in alloys, adsorbates, ferroelectrics, magnetic systems, and polytypes.		The '''axial next-nearest neighbour Ising''' (ANNNI) model <ref>[http://dx.doi.org/10.1016/0370-1573(88)90140-8 Walter Selke "The ANNNI model — Theoretical analysis and experimental application", Physics Reports '''170''' pp. 213-264 (1988)]</ref> is used to study spatially modulated structures in alloys, adsorbates, ferroelectrics, magnetic systems, and polytypes.

Carl McBride: Added 3D critical exponents

2011-07-26T10:12:30Z

Added 3D critical exponents

@@ Line 41: / Line 41: @@
 <ref>[http://www.sandia.gov/LabNews/LN04-21-00/sorin_story.html Three-dimensional proof for Ising model impossible, Sandia researcher claims to have shown]</ref>
 <ref>[http://dx.doi.org/10.1145/335305.335316    	Sorin Istrail 	 "Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces", Proceedings of the thirty-second annual ACM symposium on Theory of computing pp. 87-96   (2000)]</ref>
 ==ANNNI model==
 The '''axial next-nearest neighbour Ising''' (ANNNI) model <ref>[http://dx.doi.org/10.1016/0370-1573(88)90140-8  Walter Selke "The ANNNI model — Theoretical analysis and experimental application", Physics Reports  '''170''' pp. 213-264 (1988)]</ref> is used to study spatially modulated structures in alloys, adsorbates, ferroelectrics, magnetic systems, and polytypes.

Carl McBride: /* Critical exponents */ Added an internal link

2011-07-20T13:26:01Z

Critical exponents: Added an internal link

← Older revision		Revision as of 15:26, 20 July 2011
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	*Magnetic order parameter exponent <math>\beta = \frac{1}{8}</math> (Baxter Eq. 7.12.14)		*Magnetic order parameter exponent <math>\beta = \frac{1}{8}</math> (Baxter Eq. 7.12.14)
	*Susceptibility exponent <math>\gamma = \frac{7}{4} </math> (Baxter Eq. 7.12.15)		*Susceptibility exponent <math>\gamma = \frac{7}{4} </math> (Baxter Eq. 7.12.15)
			(see also: [[Universality classes#Ising \| Ising universality class]])

	==3-dimensional Ising model==		==3-dimensional Ising model==

Carl McBride: Started "Cellular automata" subsection

2011-07-15T10:14:39Z

Started "Cellular automata" subsection

← Older revision		Revision as of 12:14, 15 July 2011
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	==ANNNI model==		==ANNNI model==
	The '''axial next-nearest neighbour Ising''' (ANNNI) model <ref>[http://dx.doi.org/10.1016/0370-1573(88)90140-8 Walter Selke "The ANNNI model — Theoretical analysis and experimental application", Physics Reports '''170''' pp. 213-264 (1988)]</ref> is used to study spatially modulated structures in alloys, adsorbates, ferroelectrics, magnetic systems, and polytypes.		The '''axial next-nearest neighbour Ising''' (ANNNI) model <ref>[http://dx.doi.org/10.1016/0370-1573(88)90140-8 Walter Selke "The ANNNI model — Theoretical analysis and experimental application", Physics Reports '''170''' pp. 213-264 (1988)]</ref> is used to study spatially modulated structures in alloys, adsorbates, ferroelectrics, magnetic systems, and polytypes.
			==Cellular automata==
			The Ising model can be studied using cellular automata <ref>[http://dx.doi.org/10.1016/0167-2789(84)90253-7 Gérard Y. Vichniac "Simulating physics with cellular automata", Physica D: Nonlinear Phenomena '''10''' pp. 96-116 (1984)]</ref><ref>[http://dx.doi.org/10.1088/0305-4470/17/8/004 Y. Pomeau "Invariant in cellular automata", Journal of Physics A '''17''' pp. L415-L418 (1984)]</ref><ref>[http://dx.doi.org/10.1007/BF01033083 H. J. Herrmann "Fast algorithm for the simulation of Ising models", Journal of Statistical Physics '''45''' pp. 145-151 (1986)]</ref><ref>[http://dx.doi.org/10.1016/S0003-4916(86)80006-9 Michael Creutz "Deterministic ising dynamics", Annals of Physics '''167''' pp. 62-72 (1986)]</ref>.
	==See also==		==See also==
	*[[Critical exponents]]		*[[Critical exponents]]

Carl McBride: Added an external link to Scholarpedia

2011-02-10T14:37:28Z

Added an external link to Scholarpedia

← Older revision		Revision as of 16:37, 10 February 2011
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	==References==		==References==
	<references/>		<references/>
			==External links==
			*[http://dx.doi.org/10.4249/scholarpedia.10313 Barry McCoy "Ising model: exact results", Scholarpedia, 5(7):10313 (2010)]
	[[Category: Models]]		[[Category: Models]]

134.130.4.242: ANNNI model

2010-06-07T21:39:39Z

ANNNI model

← Older revision		Revision as of 23:39, 7 June 2010
Line 41:		Line 41:
	<ref>[http://dx.doi.org/10.1145/335305.335316 Sorin Istrail "Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces", Proceedings of the thirty-second annual ACM symposium on Theory of computing pp. 87-96 (2000)]</ref>		<ref>[http://dx.doi.org/10.1145/335305.335316 Sorin Istrail "Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces", Proceedings of the thirty-second annual ACM symposium on Theory of computing pp. 87-96 (2000)]</ref>
	==ANNNI model==		==ANNNI model==
	The '''axial next-nearest neighbour Ising''' (ANNNI) model <ref>[http://dx.doi.org/10.1016/0370-1573(88)90140-8 Walter Selke "The ANNNI model — Theoretical analysis and experimental application", Physics Reports '''170''' pp. 213-264 (1988)]</ref> is used to study alloys, adsorbates, ferroelectrics, magnetic systems, and polytypes.		The '''axial next-nearest neighbour Ising''' (ANNNI) model <ref>[http://dx.doi.org/10.1016/0370-1573(88)90140-8 Walter Selke "The ANNNI model — Theoretical analysis and experimental application", Physics Reports '''170''' pp. 213-264 (1988)]</ref> is used to study spatially modulated structures in alloys, adsorbates, ferroelectrics, magnetic systems, and polytypes.
	==See also==		==See also==
	*[[Critical exponents]]		*[[Critical exponents]]