Effective field theory forHe4

Abstract

We introduce an effective scalar field theory to describe the 4 He phase diagram, which can be considered as a generalization of the XY model which gives the usual λ-transition. This theory results from a Ginzburg-Landau Hamiltonian with higher order derivatives, which allow to produce transitions between the superfluid, normal liquid and solid phases of 4 He. Mean field and Monte Carlo analyses suggest that this model is able to reproduce the main qualitative features of 4 He phase transitions.

Triple point in theO(2)ghost model with higher-order gradient term

“…Therefore, we define the singularity scale as k s = k c for the cases with s − (Λ) > 0 and k s = Λ for cases with s − (Λ) < 0. If there is a singularity then TLR is applied for scales k < k s in order to determine the RG flow in the IR regime by means of the recursion relation (8) rewritten in terms of the dimensionless quantities. The scale k has then been decreased from the scale k s by at least two orders of magnitude with the step size ∆k/k = 0.005 and the truncation M = 10.…”

“…In general, field theory models with higher-derivative terms of alternating signs have rather rich phase structure corresponding to various periodic structures [4][5][6][7]. Existence of the triple point in ordinary O(2) symmetric models with appropriate higher-derivative terms has also been shown in [8].…”

Model of a scalar field coupled to its gradients

“…Explicit physical results can be also obtained in terms of the model that takes into account higher-derivative terms in a formal expansion of the relevant free-energy functional [7,8]. In the effective field theories, terms of this type are usually given rise to by the contribution of higherenergy modes.…”

“…In this paper, along with introducing a competing gradient of the order parameter in strongly correlated electronic systems, we also reveal a possibility of the non-uniform pattern formation. Introducing higher-order terms makes it possible to explain the transition between the superfluid, normal liquid, and solid phase of He 4 [7,10]. In the article [11], a possible way is proposed to describe the first-order phase transition with pattern formation in terms of the model with coupling between the order parameter and its gradient.…”