https://doi.org/10.1140/epjb/e2007-00355-4
Critical temperature for first-order phase transitions in confined systems
1
Instituto de Física, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier, 524, 20559-900 Rio de Janeiro, RJ, Brazil
2
Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil
3
Instituto de Física Teorica-IFT/UNESP Rua Pamplona 145, 01405-900 São Paulo, SP, Brazil
Corresponding author: a roditi@cbpf.br
Received:
15
May
2007
Revised:
2
October
2007
Published online:
22
December
2007
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 x1, x2, ..., xd. The planes in each pair are separated by distances L1, L2, ... , Ld. We obtain an expression for the transition temperature as a function of the size of the system, Tc({Li}), i = 1, 2, ..., d. For D = 3 we particularize this formula, taking L1 = L2 = ... = Ld = 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.
PACS: 03.70.+k – Theory of quantized fields / 11.10.-z – Field theory
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007