Critical Binder cumulant for isotropic Ising models on square and triangular lattices

TL;DR

This study uses Monte Carlo simulations to analyze the critical Binder cumulant in isotropic Ising models on square and triangular lattices, revealing its dependence on shape and boundary conditions but not on lattice type.

Contribution

It demonstrates that the critical Binder cumulant depends on shape and boundary conditions but is independent of lattice structure in isotropic short-range Ising models.

Findings

U* depends on aspect ratio for rectangular shapes

U* depends on boundary conditions and shape

U* is independent of lattice type

Abstract

Using Monte Carlo techniques, the critical Binder cumulant U* of isotropic nearest-neighbour Ising models on square and triangular lattices is studied. For rectangular shapes, employing periodic boundary conditions, U* is found to show the same dependence on the aspect ratio for both lattice types. Similarly, applying free boundary conditions for systems with square as well as circular shapes for both lattices, the simulational findings are also consistent with the suggestion that, for isotropic Ising models with short-range interactions, U* depends on the shape and the boundary condition, but not on the lattice structure.