Critical temperature for first-order phase transitions in confined systems

C. A. Linhares, A. P.C. Malbouisson, Y. W. Milla and I. Roditi ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2007, vol. 60, issue 3, 353-362

Abstract: We consider the Euclidean D-dimensional -λ|ϕ | 4 +η|ϕ| 6 (λ,η>0) model with d (d ≤ D) compactified dimensions. Introducing temperature by means of the Ginzburg–Landau prescription in the mass term of the Hamiltonian, this model can be interpreted as describing a first-order phase transition for a system in a region of the D-dimensional space, limited by d pairs of parallel planes, orthogonal to the coordinates axis x 1 , x 2 , ..., x d . The planes in each pair are separated by distances L 1 , L 2 , ... , L d . We obtain an expression for the transition temperature as a function of the size of the system, T c ({L i }), i=1, 2, ..., d. For D=3 we particularize this formula, taking L 1 =L 2 =...=L d =L for the physically interesting cases d=1 (a film), d=2 (an infinitely long wire having a square cross-section), and for d=3 (a cube). For completeness, the corresponding formulas for second-order transitions are also presented. Comparison with experimental data for superconducting films and wires shows qualitative agreement with our theoretical expressions. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Keywords: 03.70.+k Theory of quantized fields; 11.10.-z Field theory (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1140/epjb/e2007-00355-4

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