Finite-size scaling and conformal anomaly of the Ising model in curved space

TL;DR

This paper investigates the finite-size scaling and conformal anomaly of the Ising model on curved lattices with tetrahedral and octahedral topologies, confirming theoretical predictions about logarithmic corrections and anomaly contributions.

Contribution

It introduces a method to analyze the Ising model's free energy on curved spaces without changing curvature distribution, and verifies conformal field theory predictions.

Findings

Logarithmic dependence of subleading free energy contributions.

Conformal anomaly sum over conical singularities.

Frustration affects the conformal anomaly contributions.

Abstract

We study the finite-size scaling of the free energy of the Ising model on lattices with the topology of the tetrahedron and the octahedron. Our construction allows to perform changes in the length scale of the model without altering the distribution of the curvature in the space. We show that the subleading contribution to the free energy follows a logarithmic dependence, in agreement with the conformal field theory prediction. The conformal anomaly is given by the sum of the contributions computed at each of the conical singularities of the space, except when perfect order of the spins is precluded by frustration in the model.