TY - JOUR

T1 - Bound-state energy of the three-dimensional Ising model in the broken-symmetry phase

T2 - Suppressed finite-size corrections

AU - Nishiyama, Yoshihiro

PY - 2008/5/13

Y1 - 2008/5/13

N2 - 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 m2 (<2 m1) (m1: elementary excitation gap). It is expected that the ratio m2 / m1 is a universal constant in the vicinity of the critical point. In order to estimate m2 / m1, we perform a numerical diagonalization for finite clusters with N≤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 m2 / m1 =1.84 (3).

AB - 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 m2 (<2 m1) (m1: elementary excitation gap). It is expected that the ratio m2 / m1 is a universal constant in the vicinity of the critical point. In order to estimate m2 / m1, we perform a numerical diagonalization for finite clusters with N≤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 m2 / m1 =1.84 (3).

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U2 - 10.1103/PhysRevE.77.051112

DO - 10.1103/PhysRevE.77.051112

M3 - Article

AN - SCOPUS:43949130444

SN - 1539-3755

VL - 77

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 5

M1 - 051112

ER -