Finite-size scaling in anisotropic systems

Tonchev, N. S.

doi:10.1103/physreve.75.031110

Cited by 10 publications

(9 citation statements)

References 29 publications

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“…(We do not consider strongly anisotropic systems with critical exponents different from those of the usual (d, n) universality classes, see e.g. [26].) Non-cubic anisotropy effects in crystals with cubic symmetry can be easily generated by applying shear forces.…”

Section: Introductionmentioning

confidence: 99%

Diversity of critical behavior within a universality class

Dohm

2008

Phys. Rev. E

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We study spatial anisotropy effects on the bulk and finite-size critical behavior of the O(n) symmetric anisotropic phi;{4} lattice model with periodic boundary conditions in a d -dimensional hypercubic geometry above, at, and below Tc. The absence of two-scale factor universality is discussed for the bulk order-parameter correlation function, the bulk scattering intensity, and for several universal bulk amplitude relations. The anisotropy parameters are observable by scattering experiments at Tc. For the confined system, renormalization-group theory within the minimal subtraction scheme at fixed dimension d for 2

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Section: Introductionmentioning

confidence: 99%

Diversity of critical behavior within a universality class

Dohm

2008

Phys. Rev. E

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“…In such a case, it is known that a usual finite-size scaling (FSS) analysis is inapplicable, but a FSS analysis with careful consideration of the anisotropy is required. [41][42][43] Since our model possibly requires such a special FSS analysis, we check the anisotropy of the system by calculating correlation lengths which are dependent on the anisotropy. Using the Ornstein-Zernike formula, 44) correlation lengths are estimated by ratio of structure factor amplitudes.…”

Section: First-order Phase Transitionmentioning

confidence: 99%

First-Order Phase Transition with Breaking of Lattice Rotation Symmetry in Continuous-Spin Model on Triangular Lattice

Kawashima

2011

J. Phys. Soc. Jpn.

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Using a Monte Carlo method, we study the finite-temperature phase transition in the twodimensional classical Heisenberg model on a triangular lattice with or without easy-plane anisotropy. The model takes account of competing interactions: a ferromagnetic nearestneighbor interaction J1 and an antiferromagnetic third nearest-neighbor interaction J3. As a result, the ground state is a spiral spin configuration for −4 < J1/J3 < 0. In this structure, global spin rotation cannot compensate for the effect of 120-degree lattice rotation, in contrast to the conventional 120-degree structure of the nearest-neighbor interaction model. We find that this model exhibits a first-order phase transition with breaking of the lattice rotation symmetry at a finite temperature. The transition is characterized as a Z2 vortex dissociation in the isotropic case, whereas it can be viewed as a Z vortex dissociation in the anisotropic case. Remarkably, the latter is continuously connected to the former as the magnitude of anisotropy decreases, in contrast to the recent work by Misawa and Motome [J. Phys. Soc. Jpn. 79 (2010) 073001.] in which both the transitions were found to be continuous.

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“…We do not consider complications arising from strong anisotropies [20], from subleading long-range interactions [19,21], or from scaling violations for largex arising in a region of large L for fixed ξ L that manifest themselves in a nonuniform convergence of the leading singular part of free energy densities towards the respective scaling function in the asymptotic critical domain [22]. This work is structured as follows.…”

Section: Introductionmentioning

confidence: 99%

Universal anisotropic finite-size critical behavior of the two-dimensional Ising model on a strip and ofd-dimensional models on films

Kastening

2012

Phys. Rev. E

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Anisotropy effects on the finite-size critical behavior of a two-dimensional Ising model on a general triangular lattice in an infinite-strip geometry with periodic, antiperiodic, and free boundary conditions (bc) in the finite direction are investigated. Exact results are obtained for the scaling functions of the finite-size contributions to the free energy density. With ξ(>) the largest and ξ(<) the smallest bulk correlation length at a given temperature near criticality, we find that the dependence of these functions on the ratio ξ(<)/ξ(>) and on the angle parametrizing the orientation of the correlation volume is of geometric nature. Since the scaling functions are independent of the particular microscopic realization of the anisotropy within the two-dimensional Ising model, our results provide a limited verification of universality. We explain our observations by considering finite-size scaling of free energy densities of general weakly anisotropic models on a d-dimensional film (i.e., in an L×∞(d-1) geometry) with bc in the finite direction that are invariant under a shear transformation relating the anisotropic and isotropic cases. This allows us to relate free energy scaling functions in the presence of an anisotropy to those of the corresponding isotropic system. We interpret our results as a simple and transparent case of anisotropic universality, where, compared to the isotropic case, scaling functions depend additionally on the shape and orientation of the correlation volume. We conjecture that this universality extends to cases where the geometry and/or the bc are not invariant under the shear transformation and argue in favor of validity of two-scale factor universality for weakly anisotropic systems.

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Finite-size scaling in anisotropic systems

Cited by 10 publications

References 29 publications

Diversity of critical behavior within a universality class

Diversity of critical behavior within a universality class

First-Order Phase Transition with Breaking of Lattice Rotation Symmetry in Continuous-Spin Model on Triangular Lattice

Universal anisotropic finite-size critical behavior of the two-dimensional Ising model on a strip and ofd-dimensional models on films

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