Heisenberg model - Revision history

60.111.245.26: small correction.

2021-04-09T06:27:10Z

small correction.

← Older revision		Revision as of 08:27, 9 April 2021
Line 5:		Line 5:

	where the sum runs over all pairs of nearest neighbour spins, <math>\mathbf{S}</math>, and where <math>J</math> is the coupling constant.		where the sum runs over all pairs of nearest neighbour spins, <math>\mathbf{S}</math>, and where <math>J</math> is the coupling constant.
	The classical model is known to have a phase transition in three or higher spacial dimensions, and the ferromagnetic (<math>J>0</math>) and antiferromagnetic (<math>J<0</math>) share essentially the same physics.		The classical model is known to have a finite-temperature phase transition in three or higher spacial dimensions, and the ferromagnetic (<math>J>0</math>) and antiferromagnetic (<math>J<0</math>) share essentially the same physics.
	The quantum version differs greatly, and even the one-dimensional case has a rich variety of phenomena depending on the spin number <math>S</math> and the sign of <math>J</math>.		The quantum version differs greatly, and even the one-dimensional case has a rich variety of phenomena depending on the spin number <math>S</math> and the sign of <math>J</math>.

60.111.245.26: Added a very minimal ad brief explanation of the features of the model.

2021-04-09T06:26:15Z

Added a very minimal ad brief explanation of the features of the model.

← Older revision		Revision as of 08:26, 9 April 2021
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	:<math>H = -J{\sum}_{\langle i,j\rangle}\mathbf{S}_i \cdot \mathbf{S}_{j}</math>		:<math>H = -J{\sum}_{\langle i,j\rangle}\mathbf{S}_i \cdot \mathbf{S}_{j}</math>

	where the sum runs over all pairs of nearest neighbour spins, <math>\mathbf{S}</math>, and where <math>J</math> is the coupling constant.		where the sum runs over all pairs of nearest neighbour spins, <math>\mathbf{S}</math>, and where <math>J</math> is the coupling constant.
			The classical model is known to have a phase transition in three or higher spacial dimensions, and the ferromagnetic (<math>J>0</math>) and antiferromagnetic (<math>J<0</math>) share essentially the same physics.
			The quantum version differs greatly, and even the one-dimensional case has a rich variety of phenomena depending on the spin number <math>S</math> and the sign of <math>J</math>.

	==See also==		==See also==
	*[[Ising Models]] (n=1)		*[[Ising Models]] (n=1)

Carl McBride at 15:23, 22 January 2008

2008-01-22T15:23:23Z

← Older revision		Revision as of 17:23, 22 January 2008
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	{{Stub-general}}		{{Stub-general}}
			The '''Heisenberg model''' is the n=3 case of the ''n''-vector model. The [[Hamiltonian]] is given by

			:<math>H = -J{\sum}_{\langle i,j\rangle}\mathbf{S}_i \cdot \mathbf{S}_{j}</math>

			where the sum runs over all pairs of nearest neighbour spins, <math>\mathbf{S}</math>, and where <math>J</math> is the coupling constant.
	==See also==		==See also==
			*[[Ising Models]] (n=1)
			*[[XY model]] (n=2)
	*[[Mermin-Wagner theorem]]		*[[Mermin-Wagner theorem]]
	==References==		==References==

Carl McBride at 13:57, 20 November 2007

2007-11-20T13:57:23Z

← Older revision		Revision as of 15:57, 20 November 2007
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	#[http://dx.doi.org/10.1016/0031-8914(64)90223-X A. C. Hewson and D. Ter Haar "On the theory of the Heisenberg ferromagnet", Physica '''30''' pp. 271-276 (1964)]		#[http://dx.doi.org/10.1016/0031-8914(64)90223-X A. C. Hewson and D. Ter Haar "On the theory of the Heisenberg ferromagnet", Physica '''30''' pp. 271-276 (1964)]
	#[http://dx.doi.org/10.1063/1.335131 T. M. Giebultowicz and J. K. Furdyna "Monte Carlo simulation of fcc Heisenberg antiferromagnet with nearest- and next-nearest-neighbor interactions", Journal of Applied Physics '''57''' pp. 3312-3314 (1985)]		#[http://dx.doi.org/10.1063/1.335131 T. M. Giebultowicz and J. K. Furdyna "Monte Carlo simulation of fcc Heisenberg antiferromagnet with nearest- and next-nearest-neighbor interactions", Journal of Applied Physics '''57''' pp. 3312-3314 (1985)]
			#[http://dx.doi.org/10.1103/PhysRevLett.80.3535 F. Lado and E. Lomba "Heisenberg Spin Fluid in an External Magnetic Field ", Physical Review Letters '''80''' pp. 3535-3538 (1998)]
	#[http://dx.doi.org/10.1140/epjb/e2003-00246-8 E. Lomba, C. Martín and N.G. Almarza "Theory and simulation of positionally frozen Heisenberg spin systems", The European Physical Journal B '''34''' pp. 473-478 (2003)]		#[http://dx.doi.org/10.1140/epjb/e2003-00246-8 E. Lomba, C. Martín and N.G. Almarza "Theory and simulation of positionally frozen Heisenberg spin systems", The European Physical Journal B '''34''' pp. 473-478 (2003)]
	[[Category: Magnetism]]		[[Category: Magnetism]]
	[[Category: Models]]		[[Category: Models]]

Carl McBride at 13:35, 20 November 2007

2007-11-20T13:35:05Z

← Older revision		Revision as of 15:35, 20 November 2007
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	{{Stub-general}}		{{Stub-general}}
	[[~~Category: Models~~]]		==See also==
			*[[Mermin-Wagner theorem]]
	==References==		==References==
	#[http://dx.doi.org/10.1016/0031-8914(64)90223-X A. C. Hewson and D. Ter Haar "On the theory of the Heisenberg ferromagnet", Physica '''30''' pp. 271-276 (1964)]		#[http://dx.doi.org/10.1016/0031-8914(64)90223-X A. C. Hewson and D. Ter Haar "On the theory of the Heisenberg ferromagnet", Physica '''30''' pp. 271-276 (1964)]
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	#[http://dx.doi.org/10.1140/epjb/e2003-00246-8 E. Lomba, C. Martín and N.G. Almarza "Theory and simulation of positionally frozen Heisenberg spin systems", The European Physical Journal B '''34''' pp. 473-478 (2003)]		#[http://dx.doi.org/10.1140/epjb/e2003-00246-8 E. Lomba, C. Martín and N.G. Almarza "Theory and simulation of positionally frozen Heisenberg spin systems", The European Physical Journal B '''34''' pp. 473-478 (2003)]
	[[Category: Magnetism]]		[[Category: Magnetism]]
			[[Category: Models]]

Nice and Tidy at 10:36, 27 September 2007

2007-09-27T10:36:55Z

← Older revision		Revision as of 12:36, 27 September 2007
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			{{Stub-general}}
	[[Category: Models]]		[[Category: Models]]
	==References==		==References==

Carl McBride at 12:54, 24 April 2007

2007-04-24T12:54:16Z

← Older revision		Revision as of 14:54, 24 April 2007
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	==References==		==References==
	#[http://dx.doi.org/10.1016/0031-8914(64)90223-X A. C. Hewson and D. Ter Haar "On the theory of the Heisenberg ferromagnet", Physica '''30''' pp. 271-276 (1964)]		#[http://dx.doi.org/10.1016/0031-8914(64)90223-X A. C. Hewson and D. Ter Haar "On the theory of the Heisenberg ferromagnet", Physica '''30''' pp. 271-276 (1964)]
	~~#[http://dx.doi.org/~~
	#[http://dx.doi.org/10.1063/1.335131 T. M. Giebultowicz and J. K. Furdyna "Monte Carlo simulation of fcc Heisenberg antiferromagnet with nearest- and next-nearest-neighbor interactions", Journal of Applied Physics '''57''' pp. 3312-3314 (1985)]		#[http://dx.doi.org/10.1063/1.335131 T. M. Giebultowicz and J. K. Furdyna "Monte Carlo simulation of fcc Heisenberg antiferromagnet with nearest- and next-nearest-neighbor interactions", Journal of Applied Physics '''57''' pp. 3312-3314 (1985)]
	#[http://dx.doi.org/10.1140/epjb/e2003-00246-8 E. Lomba, C. Martín and N.G. Almarza "Theory and simulation of positionally frozen Heisenberg spin systems", The European Physical Journal B '''34''' pp. 473-478 (2003)]		#[http://dx.doi.org/10.1140/epjb/e2003-00246-8 E. Lomba, C. Martín and N.G. Almarza "Theory and simulation of positionally frozen Heisenberg spin systems", The European Physical Journal B '''34''' pp. 473-478 (2003)]
	[[Category: Magnetism]]		[[Category: Magnetism]]

Carl McBride at 12:54, 24 April 2007

2007-04-24T12:54:08Z

← Older revision		Revision as of 14:54, 24 April 2007
Line 1:		Line 1:
	[[Category: Models]]		[[Category: Models]]
	==References==		==References==
			#[http://dx.doi.org/10.1016/0031-8914(64)90223-X A. C. Hewson and D. Ter Haar "On the theory of the Heisenberg ferromagnet", Physica '''30''' pp. 271-276 (1964)]
			#[http://dx.doi.org/
	#[http://dx.doi.org/10.1063/1.335131 T. M. Giebultowicz and J. K. Furdyna "Monte Carlo simulation of fcc Heisenberg antiferromagnet with nearest- and next-nearest-neighbor interactions", Journal of Applied Physics '''57''' pp. 3312-3314 (1985)]		#[http://dx.doi.org/10.1063/1.335131 T. M. Giebultowicz and J. K. Furdyna "Monte Carlo simulation of fcc Heisenberg antiferromagnet with nearest- and next-nearest-neighbor interactions", Journal of Applied Physics '''57''' pp. 3312-3314 (1985)]
	#[http://dx.doi.org/10.1140/epjb/e2003-00246-8 E. Lomba, C. Martín and N.G. Almarza "Theory and simulation of positionally frozen Heisenberg spin systems", The European Physical Journal B '''34''' pp. 473-478 (2003)]		#[http://dx.doi.org/10.1140/epjb/e2003-00246-8 E. Lomba, C. Martín and N.G. Almarza "Theory and simulation of positionally frozen Heisenberg spin systems", The European Physical Journal B '''34''' pp. 473-478 (2003)]
	[[Category: Magnetism]]		[[Category: Magnetism]]

Carl McBride at 12:44, 24 April 2007

2007-04-24T12:44:42Z

← Older revision		Revision as of 14:44, 24 April 2007
Line 1:		Line 1:
	[[Category: Models]]		[[Category: Models]]
	==References=		==References==
			#[http://dx.doi.org/10.1063/1.335131 T. M. Giebultowicz and J. K. Furdyna "Monte Carlo simulation of fcc Heisenberg antiferromagnet with nearest- and next-nearest-neighbor interactions", Journal of Applied Physics '''57''' pp. 3312-3314 (1985)]
	#[http://dx.doi.org/10.1140/epjb/e2003-00246-8 E. Lomba, C. Martín and N.G. Almarza "Theory and simulation of positionally frozen Heisenberg spin systems", The European Physical Journal B '''34''' pp. 473-478 (2003)]		#[http://dx.doi.org/10.1140/epjb/e2003-00246-8 E. Lomba, C. Martín and N.G. Almarza "Theory and simulation of positionally frozen Heisenberg spin systems", The European Physical Journal B '''34''' pp. 473-478 (2003)]
	[[Category: Magnetism]]		[[Category: Magnetism]]

Carl McBride at 12:42, 24 April 2007

2007-04-24T12:42:35Z

← Older revision		Revision as of 14:42, 24 April 2007
Line 1:		Line 1:
	[[Category: Models]]		[[Category: Models]]
			==References=
			#[http://dx.doi.org/10.1140/epjb/e2003-00246-8 E. Lomba, C. Martín and N.G. Almarza "Theory and simulation of positionally frozen Heisenberg spin systems", The European Physical Journal B '''34''' pp. 473-478 (2003)]
	[[Category: Magnetism]]		[[Category: Magnetism]]