# Hierarchy of the low-lying excitations for the $(2+1)$-dimensional $q=3$ Potts model in the ordered phase

## TL;DR

This paper investigates the low-energy excitation spectrum of the 2+1 dimensional q=3 Potts model in the ordered phase using exact diagonalization, revealing bound states and estimating mass gaps near the transition.

## Contribution

It provides the first detailed analysis of the low-lying excitations and bound state spectrum in the 2+1D q=3 Potts model using exact diagonalization techniques.

## Key findings

- Elementary excitations are attractive, forming bound states.
- Estimated mass gap ratios near the transition point.
- Identified a hierarchy of low-lying excitations.

## Abstract

The $(2+1)$-dimensional $q=3$ Potts model was simulated with the exact diagonalization method. In the ordered phase, the elementary excitations (magnons) are attractive, forming a series of bound states in the low-energy spectrum. We investigate the low-lying spectrum through a dynamical susceptibility, which is readily tractable with the exact diagonalization method via the continued-fraction expansion. As a result, we estimate the series of (scaled) mass gaps, $m_{2,3,4}/m_1$ ($m_1$: single-magnon mass), in proximity to the transition point.