Precise simulation of criticality in asymmetric fluids

Abstract

Extensive grand canonical Monte Carlo simulations have been performed for the hard-core square-well fluid with interaction range $b=1.5\mathrm{}\sigma .$ The critical exponent for the correlation length has been estimated in an unbiased fashion as $\nu =0.63\mathrm{}\pm 0.03$ via finite-size extrapolations of the extrema of properties measured along specially constructed, asymptotically critical loci that represent pseudosymmetry axes. The subsequent location of the critical point achieves a precision of five parts in ${10}^4$ for $T_c$ and about 0.3% for the critical density ${\rho }_c.$ The effective exponents ${\gamma }_{\mathrm{eff}}^{+}$ and ${\beta }_{\mathrm{eff}}$ indicate Ising-type critical-point values to within 2% and 5.6%, respectively, convincingly distinguishing the universality class from the “nearby” XY and $n=0\mathrm{}$ (self-avoiding walk) classes. Simulations of the heat capacity $C_V(T,\rho )$ and $d^2{p}_{\sigma }{/dT}^2,$ where $p_{\sigma }$ is the vapor pressure below $T_c,$ suggest a negative but small Yang-Yang anomaly, i.e., a specific-heat-like divergence in the corresponding chemical potential derivative ${(d}^2{\mu }_{\sigma }{/dT}^2)$ that requires a revision of the standard asymptotic scaling description of asymmetric fluids.