Abstract
A self-consistent treatment of a phase transition with a scalar order parameter in the ordered and disordered state is described. The factorization of the correlation functions in the disordered phase leads to a shift of the transition temperature, a linear divergence (ν=1) for the correlation length, a quadratic divergence (γ=2) for the susceptibility, and a finite value (α=−1) for the specific heat. In the ordered phase the factorization of the correlation functions leads to no divergences in the correlation length and susceptibility. A study of the free energy shows that order persists above the transition temperature found by assuming disorder. The requirement of thermodynamic stability induces a first-order transition at a temperature which lies between the bare transition temperature and the shifted one.
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Supported in part by NSF grant No-GP-17560.
This work is in partial fulfillment of Ph.D. requirements at Brandeis University.
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Amit, D.J., Zannetti, M. Self-consistent treatment of a phase transition. J Stat Phys 9, 1–21 (1973). https://doi.org/10.1007/BF01016794
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DOI: https://doi.org/10.1007/BF01016794