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First-order transitions, symmetry, and the Epsilon-expansion

David Mukamel, S. Krinsky, Per Bak

Published Jan 1, 1975• 0 citations
OpenAlex

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ϵ expansion for the free energy of the continuous three-state Potts model: evidence for a first-order transition

Joseph Rudnick

Low-order terms in an epsilon expansion for the free energy of the continuous three-state Potts model are displayed. The free energy has a scaling form and predicts a first-order transition to the order state. Two universal ratios are calculated to first order in epsilon from the expression. The results of this analysis are in good agreement with corresponding results of previous renormalization group analyses of the continuous Potts model.

Journal of Physics A Mathematical and General•Jul 1, 1975•44 citations

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We study the boundary extraordinary transition of a three-dimensional (3D) tricritical O(N) O ( N ) model. We first compute the mean-field Green’s function with a general coupling of |\vec \phi|^{2n} | ϕ → | 2 n (with n=3 n = 3 corresponding to the tricritical model) at the extraordinary phase transition. Then, using layer susceptibility, we obtain the boundary operator expansion for the transverse and longitudinal modes within the \epsilon=3 - d ϵ = 3 − d expansion. Based on these results, we demonstrate that the tricritical point exhibits an extraordinary transition characterized by an ordered boundary for any N N . This provides the first nontrivial example of continuous symmetry breaking in 2D in the context of boundary criticality.

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Critical-exponent renormalization and first-order transitions

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First-Order Phase Transitions

Wolfhard Janke E

Springer eBooks•Jan 1, 2003•33 citations
We study the boundary extraordinary transition of a three-dimensional (3D) tricritical O(N) O ( N ) model. We first compute the mean-field Green’s function with a general coupling of |\vec \phi|^{2n} | ϕ → | 2 n (with n=3 n = 3 corresponding to the tricritical model) at the extraordinary phase transition. Then, using layer susceptibility, we obtain the boundary operator expansion for the transverse and longitudinal modes within the \epsilon=3 - d ϵ = 3 − d expansion. Based on these results, we demonstrate that the tricritical point exhibits an extraordinary transition characterized by an ordered boundary for any N N . This provides the first nontrivial example of continuous symmetry breaking in 2D in the context of boundary criticality.