Related papers: Disordered $\lambda\varphi^{4}+\rho\varphi^{6}$ La…
In this paper we discuss a disordered $d$-dimensional Euclidean $\lambda\varphi^{4}$ model. The dominant contribution to the average free energy of this system is written as a series of the replica partition functions of the model. In each…
Recently we introduced a new technique for computing the average free energy of a system with quenched randomness. The basic tool of this technique is a distributional zeta-function. The distributional zeta-function is a complex function…
In this paper we present a new mathematical rigorous technique for computing the average free energy of a disordered system with quenched randomness, using the replicas. The basic tool of this technique is a distributional zeta-function, a…
We discuss finite-size effects in one disordered ${\lambda}{\phi}^{4}$ model defined in a $d$-dimensional Euclidean space. We consider that the scalar field satisfies periodic boundary conditions in one dimension and it is coupled with a…
We address a mean-field zero-temperature Ginzburg-Landau, or \phi^4, model subjected to quenched additive noise, which has been used recently as a framework for analyzing collective effects induced by diversity. We first make use of a…
We study the Landau model for uniaxial incommensurate-commensurate systems of the I class by keeping Umklapp terms of third and fourth order in the expansion of the free energy. It applies to systems in which the soft mode minimum lies…
An exact solution of a Landau model of an order-disorder transition with activated critical dynamics is presented. The model describes a funnel-shaped topography of the order parameter space in which the number of energy lowering…
Spontaneous C4-symmetry breaking phases are ubiquitous in layered quantum materials, and often compete with other phases such as superconductivity. Preferential suppression of the symmetry broken phases by light has been used to explain…
The $\phi^4$ model has been the "workhorse" of the classical Ginzburg--Landau phenomenological theory of phase transitions and, furthermore, the foundation for a large amount of the now-classical developments in nonlinear science. However,…
Using ultrashort laser pulses, it has become possible to probe the dynamics of long-range order in solids on microscopic timescales. In the conventional description of symmetry-broken phases within time-dependent Ginzburg-Landau theory, the…
The nonlinear $\sigma$-model for disordered interacting electrons is studied in spatial dimensions $d>4$. The critical behavior at the metal-insulator transition is determined exactly, and found to be that of a standard…
Critical fluctuations of some order parameter describing a fluid generates long-range forces between boundaries. Here, we discuss fluctuation-induced forces associated to a disordered Landau-Ginzburg model defined in a $d$-dimensional slab…
The Hubbard model is studied in which disorder is introduced by putting the on-site interaction to zero on a fraction f of (impurity) sites of a square lattice. Using Quantum Monte Carlo methods and Dynamical Mean Field theory we find that…
This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, mean-field theory is…
We consider a renewal process \tau={\tau_0,\tau_1,...} on the integers, where the law of \tau_i-\tau_{i-1} has a power-like tail P(\tau_i-\tau_{i-1}=n)=n^{-(\alpha+1)}L(n) with \alpha\ge0 and L(.) slowly varying. We then assign a random,…
We formulate a spectral problem related to the onset of superconductivity for a generalized Ginzburg-Landau model, where the order parameter and the magnetic potential are defined in the whole space. This model is devoted to the `proximity…
We consider a general model of a disordered copolymer with adsorption. This includes, as particular cases, a generalization of the copolymer at a selective interface introduced by Garel et al. [Europhys. Lett. 8 (1989) 9--13], pinning and…
We show that the limiting ground state energy of the spherical mixed p-spin model can be identified as the infimum of certain variational problem. This complements the well-known Parisi formula for the limiting free energy in the spherical…
This thesis is an attempt to provide a new outlook on complex systems, as well as some physical answers for certain models, taking a computational approach. We have focused on disordered systems, addressing two traditional problems in three…
Ginzburg-Landau model with two order parameters appears in many condensed-matter problems. However, even for scalar order parameters, the most general U(1)-symmetric Landau potential with all quadratic and quartic terms contains 13…