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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).
Using Monte Carlo simulations, finite-size effects of interfacial properties in the rough phase of the Ising on a cubic lattice with $Ltimes Ltimes R$ sites are studied. In particular, magnetization profiles perpendicular to the flat interface of siz
The statistical mechanics of a two-state Ising spin-glass model with finite random connectivity, in which each site is connected to a finite number of other sites, is extended in this work within the replica technique to study the phase transitions i
Corrections to scaling in the 3D Ising model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L. Analytical arguments show the existence of corrections with the exponent (gamm
Energy eigenvalues and order parameters are calculated by exact diagonalization for the transverse Ising model on square lattices of up to 6x6 sites. Finite-size scaling is used to estimate the critical parameters of the model, confirming universalit
Corrections to scaling in the two-dimensional scalar phi^4 model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L (from 4 to 1536) and different values of the phi^4 coupling