Abstract
We introduce a new way of reconstructing the equation of state of a thermodynamic system near a second-order critical point from a finite set of Taylor coefficients computed away from the critical point. We focus on the Ising universality class (Z_{2} symmetry) and show that, in the crossover region of the phase diagram, it is possible to efficiently extract the location of the nearest thermodynamic singularity, the Lee-Yang edge singularity, from which one can (i)determine the location of the critical point, (ii)constrain the nonuniversal parameters that maps the equation of state to that of the Ising model in the scaling regime, and (iii)numerically evaluate the equation of state in the vicinity of the critical point. This is done by using a combination of Padé resummation and conformal maps. We explicitly demonstrate these ideas in the celebrated Gross-Neveu model.
Highlights
How can we determine whether a critical point exists, and if it does, how can we reconstruct the singular behavior of the equation of state near the critical point from the truncated expansion obtained away from it?
We focus on the Ising universality class (Z2 symmetry) and show that, in the crossover region of the phase diagram, it is possible to efficiently extract the location of the nearest thermodynamic singularity, the LeeYang edge singularity, from which one can (i) determine the location of the critical point, (ii) constrain the nonuniversal parameters that maps the equation of state to that of the Ising model in the scaling regime, and (iii) numerically evaluate the equation of state in the vicinity of the critical point
Critical behavior of the system? More precisely, how can we determine whether a critical point exists, and if it does, how can we reconstruct the singular behavior of the equation of state near the critical point from the truncated expansion obtained away from it? We show that it is possible to obtain a surprisingly large amount of information about the critical behavior of the system from the series coefficients, even if we have access to a modest number of them
Summary
How can we determine whether a critical point exists, and if it does, how can we reconstruct the singular behavior of the equation of state near the critical point from the truncated expansion obtained away from it? With a finite Our goal is to number of terms: fðT; μÞ∼ extract as much information from it as possible, especially about its singular behavior near a critical point if there is one.
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