Universal critical behavior of the two-magnon-bound-state mass gap for the (2+1)-dimensional Ising model

TL;DR

This study investigates the universal ratio of the two-magnon-bound-state mass gap to the one-magnon mass gap in the (2+1)-dimensional Ising model using numerical diagonalization, confirming near-universality with refined models.

Contribution

It provides numerical evidence for the universal mass-gap ratio in the (2+1)D Ising model by suppressing scaling corrections through extended interactions.

Findings

Mass-gap ratio m_2/m_1=1.84(1) found for finite clusters.

Numerical diagonalization effectively accesses low-lying spectrum.

Results support universality near the critical point.

Abstract

The two-magnon-bound-state mass gap m_2 for the two-dimensional quantum Ising model was investigated by means of the numerical diagonalization method; the low-lying spectrum is directly accessible via the numerical diagonalization method. It has been claimed that the ratio m_2/m_1 (m_1: one-magnon mass gap) is a universal constant in the vicinity of the critical point. Aiming to suppress corrections to scaling (lattice artifact), we consider the spin-S=1 Ising model with finely-adjusted extended interactions. The simulation result for the finite-size cluster with N \le 20 spins indicates the mass-gap ratio m_2/m_1=1.84(1).