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Physics Letters A

Estimates of universal combinations between thermodynamic critical amplitudes for Ising-like systems

C. Bagnuls, Claude Bervillier, E. Boccara

Published Jul 1, 1984• 19 citations
Publisher
DOI
10.1016/0375-9601(84)90593-0

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The critical thermodynamics of the random quenched dilute Ising system is studied using a field-theoretical approach. A method of calculation of the universal critical amplitude combinations directly in three space dimensions is given. It is applied to both the disordered (T>Tc{\mathit{T}}_{\mathit{c}}Tc​) and the ordered (TTc{\mathit{T}}_{\mathit{c}}Tc​) phases. The detailed derivation of the relevant perturbative series expansions is presented up to the third order in powers of the renormalized coupling constants. Because of the shortness of the series, only indicative values for the amplitude combinations are proposed. Those estimates seem to be reliable except for the specific-heat amplitude ratio for which, however, the result suggests a positive sign.
We present estimates for the 3D Ising model on the cubic lattice, both regarding interface and bulk properties. We have results for the interface tension, in particular the amplitude sigma0 in the critical law sigma = sigma0*t**mu, and for the universal combination R_ = sigma*xi**2. Concerning the bulk properties, we estimate the specific heat universal amplitude ratio A+/A_, together with the exponent alpha, the nonsingular background of energy and specific heat at criticality, together with the exponent nu. There are also results for the universal combination fs*xi**3, where fs is the singular part of the free energy.