Bound-state energy of the d=3 Ising model in the broken-symmetry phase: Suppressed finite-size corrections

TL;DR

This study numerically investigates the bound-state energy in the 3D Ising model's broken-symmetry phase, estimating a universal mass-gap ratio with reduced finite-size effects using extended interactions.

Contribution

It introduces a numerical approach with extended interactions to accurately estimate the universal bound-state energy ratio in the 3D Ising model.

Findings

Estimated the mass-gap ratio as 1.84(3).

Reduced finite-size errors with extended interactions.

Confirmed universality of the bound-state energy ratio.

Abstract

The low-lying spectrum of the three-dimensional Ising model is investigated numerically; we made use of an equivalence between the excitation gap and the reciprocal correlation length. In the broken-symmetry phase, the magnetic excitations are attractive, forming a bound state with an excitation gap m_2(<2m_1) (m_1: elementary excitation gap). It is expected that the ratio m_2/m_1 is a universal constant in the vicinity of the critical point. In order to estimate m_2/m_1, we perform the numerical diagonalization for finite clusters with N \le 15 spins. In order to reduce the finite-size errors, we incorporated the extended (next-nearest-neighbor and four-spin) interactions. As a result, we estimate the mass-gap ratio as m_2/m_1=1.84(3).