Sensitivity of the thermodynamics of two-dimensional systems towards the topological classes of their surfaces
arXiv:2212.14358 · doi:10.1016/j.physa.2023.128960
Abstract
Using Monte Carlo simulations we study the two-dimensional Ising model on triangular, square, and hexagonal lattices with various topologies. We focus on the behavior of the magnetic susceptibility and of the specific heat near the critical point of the planar bulk system. We find that scaling functions of these quantities on the spherical surface (Euler characteristic K = 2) differ from the scaling functions on the projective plane (K = 1) which, in turn, differ from the scaling functions on the torus and on the Klein bottle (both K = 0). This provides strong evidence that phase transitions of the Ising model on two-dimensional surfaces depend on their topologies.
arXiv comment25 pages, 10 figures
References in corpus (9)
- Critical Phenomena and Renormalization-Group Theory
- Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus
- Magnetochiral symmetry breaking in a Möbius ring
- Ising model on nonorientable surfaces: Exact solution for the Moebius strip and the Klein bottle
- Finite-size scaling for the Ising model on the Moebius strip and the Klein bottle
- Exact Finite-Size-Scaling Corrections to the Critical Two-Dimensional Ising Model on a Torus
- Exact Finite-Size-Scaling Corrections to the Critical Two-Dimensional Ising Model on a Torus. II. Triangular and hexagonal lattices
- Universality of the Ising Model on Sphere-like Lattices
- Critical parameters and universal amplitude ratios of two-dimensional spin-S Ising models using high- and low-temperature expansions