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

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/m₁ (m₁: single-magnon mass), in proximity to the transition point.