A Monte Carlo analysis of the two-dimensional modified step model

Nymeyer, A

doi:10.1088/0305-4470/19/11/026

J. Phys. A: Math. Gen.

1986

DOI: 10.1088/0305-4470/19/11/026

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A Monte Carlo analysis of the two-dimensional modified step model

A Nymeyer¹

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1988

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“…If this is a relevant argument behind the BKT phase transition, then the behaviour for topological lattice actions is in fact tricky. Some time ago, the BKT phase transition has been investigated in the so-called Step Model [18][19][20][21]. The Step Model has a topological action, which vanishes if the angle between nearest-neighbour spins is less than π/2 ; otherwise it is a positive constant S 0 .…”

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Topological lattice actions for the 2d XY model

Bietenholz

Bögli

Niedermayer

et al. 2013

J. High Energ. Phys.

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We consider the 2d XY Model with topological lattice actions, which are invariant against small deformations of the field configuration. These actions constrain the angle between neighbouring spins by an upper bound, or they explicitly suppress vortices (and anti-vortices). Although topological actions do not have a classical limit, they still lead to the universal behaviour of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition -at least up to moderate vortex suppression. Thus our study underscores the robustness of universality, which persists even when basic principles of classical physics are violated. In the massive phase, the analytically known Step Scaling Function (SSF) is reproduced in numerical simulations. In the massless phase, the BKT value of the critical exponent η c is confirmed. Hence, even though for some topological actions vortices cost zero energy, they still drive the standard BKT transition. In addition we identify a vortex-free transition point, which deviates from the BKT behaviour.

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confidence: 99%

“…Also the version with a finite step at a variable angle has been addressed with analytical approaches[19,20].…”

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confidence: 99%

Topological lattice actions for the 2d XY model

Bietenholz

Bögli

Niedermayer

et al. 2013

J. High Energ. Phys.

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Monte Carlo evidence of a phase transition in the two-dimensional step model

Sánchez‐Velasco

Wills

1988

Phys. Rev. B

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Using Monte Carlo techniques, we study the magnetic susceptibility and specific heat of the two-dimensional step model. Contrary to some theoretical expectations and numerical results, the finite-size-scale analysis of the susceptibility sho~s evidence for a possible low-temperature phase with in6nite correlation lengths and with a nondivergent speci6c heat. The absence in this model of long-lived metastable states is also analyzed.

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A Monte Carlo analysis of the two-dimensional modified step model

Cited by 2 publications

References 13 publications

Topological lattice actions for the 2d XY model

Topological lattice actions for the 2d XY model

Monte Carlo evidence of a phase transition in the two-dimensional step model

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