Monte Carlo analysis of critical phenomenon of the Ising model on memory stabilizer structures

TL;DR

This paper uses Monte Carlo simulations to analyze how the structure of stabilizer-based graphs influences the critical temperature and exponents of the Ising model, linking quantum error correction concepts with statistical physics.

Contribution

It introduces a novel approach by applying Monte Carlo analysis to Ising models on graphs derived from quantum stabilizer formalism, revealing the impact of generator choice on critical phenomena.

Findings

Stabilizer generator choice significantly affects critical temperature.

Graph structure influences critical exponents.

Monte Carlo methods effectively analyze quantum-inspired graph models.

Abstract

We calculate the critical temperature of the Ising model on a set of graphs representing a concatenated three-bit error-correction code. The graphs are derived from the stabilizer formalism used in quantum error correction. The stabilizer for a subspace is defined as the group of Pauli operators whose eigenvalues are +1 on the subspace. The group can be generated by a subset of operators in the stabilizer, and the choice of generators determines the structure of the graph. The Wolff algorithm, together with the histogram method and finite-size scaling, is used to calculate both the critical temperature and the critical exponents of each structure. The simulations show that the choice of stabilizer generators, both the number and the geometry, has a large effect on the critical temperature.