No Arabic abstract
In this paper we investigate bubble nucleation in a disordered Landau-Ginzburg model. First we adopt the standard procedure to average over the disordered free energy. This quantity is represented as a series of the replica partition functions of the system. Using the saddle-point equations in each replica partition function, we discuss the presence of a spontaneous symmetry breaking mechanism. The leading term of the series is given by a large-N Euclidean replica field theory. Next, we consider finite temperature effects. Below some critical temperature, there are N real instantons-like solutions in the model. The transition from the false to the true vacuum for each replica field is given by the nucleation of a bubble of the true vacuum. In order to describe these irreversible processes of multiple nucleation, going beyond the diluted instanton approximation, an effective model is constructed, with one single mode of a bosonic field interacting with a reservoir of N identical two-level systems.
We discuss a disordered $lambdavarphi^{4}+rhovarphi^{6}$ Landau-Ginzburg model defined in a d-dimensional space. First we adopt the standard procedure of averaging the disorder dependent free energy of the model. The dominant contribution to this quantity is represented by a series of the replica partition functions of the system. Next, using the replica symmetry ansatz in the saddle-point equations, we prove that the average free energy represents a system with multiple ground states with different order parameters. For low temperatures we show the presence of metastable equilibrium states for some replica fields for a range of values of the physical parameters. Finally, going beyond the mean-field approximation, the one-loop renormalization of this model is performed, in the leading order replica partition function.
We discuss fluctuation-induced forces in a system described by a continuous Landau-Ginzburg model with a quenched disorder field, defined in a $d$-dimensional slab geometry $mathbb R^{d-1}times[0,L]$. A series representation for the quenched free energy in terms of the moments of the partition function is presented. In each moment an order parameter-like quantity can be defined, with a particular correlation length of the fluctuations. For some specific strength of the non-thermal control parameter, it appears a moment of the partition function where the fluctuations associated to the order parameter-like quantity becomes long-ranged. In this situation, these fluctuations become sensitive to the boundaries. In the Gaussian approximation, using the spectral zeta-function method, we evaluate a functional determinant for each moment of the partition function. The analytic structure of each spectral zeta-function depending on the dimension of the space for the case of Dirichlet, Neumann Laplacian and also periodic boundary conditions is discussed in a unified way. Considering the moment of the partition function with the largest correlation length of the fluctuations, we evaluate the induced force between the boundaries, for Dirichlet boundary conditions. We prove that the sign of the fluctuation-induced force for this case depend in a non-trivial way on the strength of the non-thermal control parameter.
The perturbative renormalization of the Ginzburg-Landau model is reconsidered based on the Feynman diagram technique. We derive renormalization group (RG) flow equations, exactly calculating all vertices appearing in the perturbative renormalization of the phi^4 model up to the epsilon^3 order of the epsilon-expansion. In this case, the phi^2, phi^4, phi^6, and phi^8 vertices appear. All these vertices are relevant. We have tested the expected basic properties of the RG flow, such as the semigroup property. Under repeated RG transformation R_s, appropriately represented RG flow on the critical surface converges to certain s-independent fixed point. The Fourier-transformed two-point correlation function G(k) has been considered. Although the epsilon-expansion of X(k)=1/G(k) is well defined on the critical surface, we have revealed an inconsistency of the perturbative method with the exact rescaling of X(k), represented as an expansion in powers of k at k --> 0. We have discussed also some aspects of the perturbative renormalization of the two-point correlation function slightly above the critical point. Apart from the epsilon-expansion, we have tested and briefly discussed also a modified approach, where the phi^4 coupling constant u is the expansion parameter at a fixed spatial dimensionality d.
Searching for characteristic signatures of a higher order phase transition (specifically of order three or four), we have calculated the spatial profiles and the energies of a spatially varying order parameter in one dimension. In the case of a $p^{th}$ order phase transition to a superconducting ground state, the free energy density depends on temperature as $a^p$, where $a = a_o(1-T/T_c)$ is the reduced temperature. The energy of a domain wall between two degenerate ground states is $epsilon_p simeq a^{p-1/2}$. We have also investigated the effects of a supercurrent in a narrow wire. These effects are limited by a critical current which has a temperature dependence $J_c(T) simeq a^{(2p-1)/2}$. The phase slip center profiles and their energies are also calculated. Given the suggestion that the superconducting transtion in bkbox, for $x = 0.4$, may be of order four, these predictions have relevance for future experiments.
We present a short review of our studies of disorder influence upon Ginzburg - Landau expansion coefficients in Anderson - Hubbard model with attraction in the framework of the generalized DMFT+$Sigma$ approximation. A wide range of attractive potentials $U$ is considered - from weak coupling limit, where superconductivity is described by BCS model, to the limit of very strong coupling, where superconducting transition is related to Bose - Einstein condensation (BEC) of compact Cooper pairs, which are formed at temperatures significantly higher than the temperature of superconducting transition, as well as the wide range of disorders - from weak to strong, when the system is in the vicinity of Anderson transition. For the same range of parameters we study in detail the temperature behavior of orbital and paramagnetic upper critical field $H_{c2}(T)$, which demonstrates the anomalies both due to the growth of attractive potential and the effects of strong disordering.