Simulating the All-Order Strong Coupling Expansion I: Ising Model Demo

TL;DR

This paper explores an alternative simulation method for lattice field theories using the worm algorithm, demonstrating its effectiveness in the Ising model by maintaining signal quality at large distances and reducing critical slowing down.

Contribution

It introduces a generalized worm algorithm approach for simulating the strong coupling expansion, improving efficiency and accuracy in lattice field theory simulations.

Findings

Signal to noise ratio remains stable at large separations.

Critical slowing down is effectively eliminated.

Method successfully estimates two-point functions in the Ising model.

Abstract

We investigate in some detail an alternative simulation strategy for lattice field theory based on the so-called worm algorithm introduced by Prokof'ev and Svistunov in 2001. It amounts to stochastically simulating the strong coupling expansion rather than the usual configuration sum. A detailed error analysis and an important generalization of the method are exemplified here in the simple Ising model. It allows for estimates of the two point function where in spite of exponential decay the signal to noise ratio does not degrade at large separation. Critical slowing down is practically absent. In the outlook some thoughts on the general applicability of the method are offered.