Phase diagram of a model forHe3-He

Phase diagram of a model for ^{3}He-^{4}He mixtures in three dimensions

“…In d = 2 the phase diagram of the VBEG model was obtained by means of the Migdal-Kadanoff renormalizationgroup method [15,16]. Its features are qualitatively similar to those observed experimentally for the corresponding three-dimensional mixtures, except that there is no true tricritical point for any value of the model parameters.…”

“…(6.14) as 15) where u i ≡ |u i | exp(iζ i ). The approximation (6.15) is a 'coarse-graining' procedure which reduces degrees of freedom.…”

“…In the temperature - 3 He concentration plane (T, x) the line of second-order superfluid transitions T s (x) meets the boundary of the two-phase coexistence region at the tricritical point (T t ≈ 87mK, x t ≈ 0.67); x = N 3 /(N 3 + N 4 ), where N i , i = 3, 4, denotes the number of atoms of 3 He or 4 He, respectively. In this paper we consider a simple lattice model known in the literature as the Vectoralized Blume-Emery-Griffiths model (VBEG) [15,16]. It is defined in Sec.…”

“…II. The bulk phase diagram of the VBEG model was investigated only in spatial dimensions d = 2 by means of Migdal-Kadanoff recursion relations [15,16]; no tricritical point was found for any value of the model parameters. Here we study the three-dimensional version of this model within the molecular-field approximation and by Monte Carlo simulations, and we demonstrate that for reasonable values of interaction parameters the resulting phase diagram resembles topologically that observed experimentally for three dimensional mixtures, for which the phase separation appears as a consequence of the superfluid ordering.…”

Phase diagram of fluid phases inHe3−He4mixtures

“…Further improvements in the theoretical description of the phase diagrams of and Scalapino [7] and, independently, by Berker and Nelson [8]. More recently it has been investigated in d=3 within mean-field theory and by Monte Carlo simulations [9].…”