Universal combination of critical amplitudes from field theory

Abstract

Near a continuous phase transition, there exist universal combinations of critical amplitudes. We present an estimation of such a universal quantity, in the framework of the ${\phi }^4$ field theory in three dimensions, using information recently available in the literature, and already used to determine precise values for critical exponents. This leads to an accuracy only obtained, hitherto, in the framework of field theory, for critical exponents. The universal quantity calculated, often denoted by $R_{\xi }^{}{}_{}{}^{+}$, combines the amplitude of the correlation length and that of the singular part of the specific heat in the vicinity of the critical point.