Diversity of critical behavior within a universality class
Volker Dohm

TL;DR
This paper investigates how spatial anisotropy influences critical behavior in the O(n) symmetric $^4$ lattice model, revealing nonuniversal effects, agreement with Monte Carlo data, and predicting measurable anisotropy-dependent features.
Contribution
It provides a detailed analysis of anisotropy effects on critical phenomena, combining renormalization-group theory with Monte Carlo data, and predicts measurable anisotropy-dependent features in finite-size scaling.
Findings
Excellent agreement with Monte Carlo data for the 3D Ising model at $T_c$
Predicted non-monotonic dependence of the Binder cumulant on NNN couplings
Identified a Lifschitz point at larger antiferromagnetic NNN coupling
Abstract
We study spatial anisotropy effects on the bulk and finite-size critical behavior of the O symmetric anisotropic lattice model with periodic boundary conditions in a -dimensional hypercubic geometry above, at and below . 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. For the confined system, renormalization-group theory within the minimal subtraction scheme at fixed dimension for is employed. For the case of cubic symmetry and for our perturbation approach yields excellent agreement with the Monte Carlo (MC) data for the finite-size amplitude of the free energy of the three-dimensional Ising model at by Mon [Phys. Rev. Lett. {\bf 54}, 2671 (1985)]. Below a minimum of the scaling function of…
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