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AIP conference proceedings

The critical renormalized coupling constants in the symmetric phase of the three dimensional Ising model

Jae-Kwon Kim

Published Jan 1, 2000• 6 citations
Publisher

Abstract

Using a novel finite size scaling Monte Carlo method, we calculate the four, six and eight point renormalized coupling constants defined at zero momentum in the symmetric phase of the three dimensional Ising system.
DOI
10.1063/1.1291592

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Using a finite-size scaling method combined with extensive Monte Carlo measurements of high statistics, we calculate the four-, six- and eight-point renormalized coupling constants defined at zero momentum in the symmetric phase of the three-dimensional Ising system. The results of the 2D Ising system that are directly measured are also reported. Our value of the four-point coupling constant for the 3D system agrees very well with the available estimates from other methods. Our values of the six- and eight-point coupling constants are significantly different from those obtained by other methods for the 3D system, although they agree reasonably well in the 2D system.
We compute the 2n-point renormalized coupling constants in the symmetric phase of the three-dimensional (3D) Ising model on the simple cubic lattice in terms of the high temperature expansions O(${\mathrm{\ensuremath{\mathrm{B}}}}^{17}$) of the Fourier transformed 2n-point connected correlation functions at zero momentum. Our high temperature estimates of these quantities, which enter into the small field expansion of the effective potential for a 3D scalar field at the infrared fixed point or, equivalently, in the critical equation of state of the 3D Ising model universality class, are compared with recent results obtained by renormalization group methods, strong coupling, stochastic simulations, as well as previous high temperature expansions.
Monte Carlo calculations of the renormalized coupling constant for the three-dimensional Ising model are reported. Improved estimators both for the second partial of the susceptibility with respect to the magnetic field and for the correlation length are developed. These estimators show greatly improved convergence properties, and allow us to compute for system sizes and temperature rather more relevant to the thermodynamic limit than previously. Our results indicate strongly that hyperscaling holds for this model.