A Monte Carlo analysis of the two-dimensional planar and step models

Nymeyer, A; Irving, A.C.

doi:10.1088/0305-4470/19/9/046

Cited by 6 publications

(5 citation statements)

References 11 publications

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“…The errors are considerably smaller than the symbols. For example, at β = 1.22 we found z 1 = 0.0024136 (7) and 0.00017902(6) at L = 32 and 128 respectively. The slope of Fig.…”

Section: Methods and Resultsmentioning

confidence: 87%

“…The analysis began with a rough search for the leading critical behaviour predicted by (8). An independent test was also made using the (less accurate) susceptibility data and (7). Both methods indicated critical behaviour setting in for β > ∼ 1.2.…”

Section: Methods and Resultsmentioning

confidence: 99%

“…In this paper we apply the same techniques to the closely related 'step model' [3,4], also known [5,6] as the sgn O(2) model. The question of criticality of this model has, until now, been unresolved despite several analyses based on high temperature series (see [6] for a review) and on numerical simulation [7,8]. The interest in the model arises from its possible membership of the XY -model universality class which exhibits the Kosterlitz-Thouless [KT] phase transition [9].…”

Section: Introductionmentioning

confidence: 99%

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Critical behavior of the two-dimensional step model

Irving

Kenna

1996

Phys. Rev. B

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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.

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“…The errors are considerably smaller than the symbols. For example, at β = 1.22 we found z 1 = 0.0024136 (7) and 0.00017902(6) at L = 32 and 128 respectively. The slope of Fig.…”

Section: Methods and Resultsmentioning

confidence: 87%

Section: Methods and Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Critical behavior of the two-dimensional step model

Irving

Kenna

1996

Phys. Rev. B

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“…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 question of criticality of this model has, until now, been unresolved despite several analyses based on high temperature series and on numerical simulation [35,36]. The interest in the model arises from its possible membership of the Kosterlitz-Thouless universality class.…”

Section: The Step Modelmentioning

confidence: 99%

The Kosterlitz-Thouless universality class

Kenna

Irving

1997

Nuclear Physics B

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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.

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