# Universality of the Ising Model on Sphere-like Lattices

## TL;DR

This study investigates the 2D Ising model on sphere-like lattices, confirming universality in critical behavior and identifying anomalies in pseudocritical coupling shifts due to topology.

## Contribution

It demonstrates the universality of the Ising model on different sphere-like topologies and uncovers topology-induced anomalies in critical coupling shifts.

## Key findings

- Partition function zeros align with expected universality scaling.
- Critical cumulants peak at values consistent with Onsager solution.
- Significant anomalies in pseudocritical coupling shifts for sphere-like lattices.

## Abstract

We study the 2D Ising model on three different types of lattices that are topologically equivalent to spheres. The geometrical shapes are reminiscent of the surface of a pillow, a 3D cube and a sphere, respectively. Systems of volumes ranging up to O($10^5$) sites are simulated and finite size scaling is analyzed. The partition function zeros and the values of various cumulants at their respective peak positions are determined and they agree with the scaling behavior expected from universality with the Onsager solution on the torus ($\nu=1$). For the pseudocritical values of the coupling we find significant anomalies indicating a shift exponent $\neq 1$ for sphere-like lattice topology.