Critical behaviour of an isotropic spin system. II

Guttman, A J; Nymeyer, A

doi:10.1088/0305-4470/11/6/014

Cited by 10 publications

(7 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The conventional picture is that the XY -model phase transition is driven by a vortex binding mechanism [3,4]. This is in contrast to the customary picture of the step model [31,32,33,34,35,36,38]. Here, while the configuration space is the same as that of the XY -model, vortex formation is not believed to be energetically favourable given the discontinuous nature of the interaction function.…”

Section: Discussionmentioning

confidence: 99%

“…The KT phase transition of the XY -model is understood to be driven by the binding/unbinding of vortices. The energetics of vortex formation in the step model are, however, very different from the XY -model [34,36,38]. Since vortices with effectively zero excitation energy can be created at all non-zero temperatures, the usual KT argument does not naturally lead one to expect such a phase transition in the step model.…”

Section: The Step Modelmentioning

confidence: 94%

“…Unlike the XY -model, however, the interaction function is discontinuous and the Mermin-Wagner theorem [1] remains unproven for this case (see however [37]). Nonetheless, it is expected that if a phase transition exists in the step model, it should not be to a phase with long range order [32,36,38]. The KT phase transition of the XY -model is understood to be driven by the binding/unbinding of vortices.…”

Section: The Step Modelmentioning

confidence: 99%

See 2 more Smart Citations

The Kosterlitz-Thouless universality class

Kenna

Irving

1997

Nuclear Physics B

View full text Add to dashboard Cite

We examine the Kosterlitz-Thouless universality class and show that essential scaling at this type of phase transition is not selfconsistent unless multiplicative logarithmic corrections are included. In the case of specific heat these logarithmic corrections are identified analytically. To identify those corresponding to the susceptibility we set up a numerical method involving the finite-size scaling of LeeYang zeroes. We also study the density of zeroes and introduce a new concept called index scaling. We apply the method to the XY -model and the closely related step model in two dimensions. The critical parameters (including logarithmic corrections) of the step model are compatable with those of the XY -model indicating that both models belong to the same universality class. This result then raises questions over how a vortex binding scenario can be the driving mechanism for the phase transition. Furthermore, the logarithmic corrections identified numerically by our methods of fitting are not in agreement with the renormalization group predictions of Kosterlitz and Thouless.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: The Step Modelmentioning

confidence: 94%

Section: The Step Modelmentioning

confidence: 99%

See 1 more Smart Citation

The Kosterlitz-Thouless universality class

Kenna

Irving

1997

Nuclear Physics B

View full text Add to dashboard Cite

show abstract

“…The KT phase transition of the XY -model is understood to be driven by the binding/unbinding of topological solutions (vortices). However, the energetics of vortex formation are very different in the step model [11,6,8]. Since vortices with effectively zero excitation energy can be created at all non-zero temperatures, the usual KT argument does not naturally lead one to expect such a phase transition in the step model.…”

Section: Discussionmentioning

confidence: 99%

“…Unlike the XY -model, however, the interaction function is discontinuous and the Mermin-Wagner theorem [10] does not apply. Nonetheless, it is expected that if a phase transition exists in the step model, it should not be to a phase with long range order [4,8,11].…”

Section: Introductionmentioning

confidence: 99%

Critical behavior of the two-dimensional step model

Irving

Kenna

1996

Phys. Rev. B

View full text Add to dashboard Cite

We use finite-size scaling of Lee-Yang partition function zeroes to study the critical behaviour of the two dimensional step or sgn O(2) model. We present evidence that, like the closely related XY -model, this has a phase transition from a disordered high temperature phase to a low temperature massless phase where the model remains critical. The critical parameters (including logarithmic corrections) are compatible with those of the XY -model indicating that both models belong to the same universality class.

show abstract

Migdal transformations of O(2)-symmetric spin Hamiltonians

Barber

1983

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

Critical behaviour of an isotropic spin system. II

Cited by 10 publications

References 6 publications

The Kosterlitz-Thouless universality class

The Kosterlitz-Thouless universality class

Critical behavior of the two-dimensional step model

Migdal transformations of O(2)-symmetric spin Hamiltonians

Contact Info

Product

Resources

About