On the equivalence of different Landau expansions

✍ Scribed by C.E.I. Carneiro; V.B. Henriques; S.R. Salinas

• Book ID: 103893774
• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 456 KB
• Volume: 162
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(89)90557-8

✦ Synopsis

The critical behavior of magnetic model systems in the mcan-lield approximation may be obtained from a standard Landau expansion, in terms of the order parameter m, of the functional 0(T. H: m)=-Hm +.f(T. m). where f i~ the Helmht;Itz free energy. As an alternative procedure, the Gibbs free energy, g(7". H). may be written as the minimum of a functional g(T, H: y) with respect to a continuous spin field v. and the critical behavior can be analysed on the basis of an expansion of this functional in powers of v. Wc show that. in spite of displaying quite distirlct coefficients, in zero ordering field, both expansions lead to the S;Jllle critical and tricritical hchaxior. We obtain relationships between these sets of coeflicicnts. for a rather general ease. and discuss, as an illustration, the simple Ising fcrromagnct. W¢ also remark that these di~tinction~ are already pre~ent in different str~itcgies to ot~tain a suital~lc Landau-(;inzhurg-V,,'il~tm I I:tmiltoni~m for performing a momentum-space renormalization-group calculation.