Related papers: Random-energy model in random fields
In this paper we look at a class of random optimization problems that arise in the forms typically known as Hopfield models. We view two scenarios which we term as the positive Hopfield form and the negative Hopfield form. For both of these…
The one-dimensional Ising model in an external magnetic field with uniform long-range interactions and random short-range interactions satisfying bimodal annealed distributions is studied. This generalizes the random model discussed by…
Here we present an explicit counterexample to a bimodality concept as the unique signal of first order phase transition. Using an exact solution of the simplified version of the statistical multifragmentation model we demonstrate that the…
A review of the present state of investigations of the pseudospin-electron model (PEM), which is used in the theory of strongly correlated electron systems, is given. The model is used to describe the systems with the locally anharmonic…
The transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in…
In view of the recently seen dramatic effect of quenched random bonds on tricritical systems, we have conducted a renormalization-group study on the effect of quenched random fields on the tricritical phase diagram of the spin-1 Ising model…
In strongly coupled field theories, perturbation theory cannot be employed to study the low-energy spectrum. Thus, non-perturbative techniques are required. We employ the variational method, a rigorous, non-perturbative approach which…
The statistical linearization method known in nonlinear mechanics and random vibrations theory has been applied to stochastically quantized fields in finite temperature. It has been shown that even in its simplest form the method yields…
The dynamics of individual colloidal particles in random potential energy landscapes were investigated experimentally and by Monte Carlo simulations. The value of the potential at each point in the two-dimensional energy landscape follows a…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
In this tutorial, we provide the natural derivation of symmetrical, gauge-invariant canonical energy-momentum tensor for the abelian gauge field, i.e., the electromagnetic field.
It is argued that continuum realisations of distributions of collisionless charged particles should accommodate a dynamically evolving number of electric currents even if the continuum is composed of only one species of particle, such as…
By applying the renormalization group method to two-coupled chains in the Tomonaga model, the role of interchain hopping has been studied in the entire energy region. The energy for a crossover from the perturbational regime to the relevant…
We introduce a massively parallel replica-exchange grand-canonical sampling algorithm to simulate materials at realistic conditions, in particular surfaces and clusters in reactive atmospheres. Its purpose is to determine in an automated…
In this thesis, we consider several Random Energy Models. This includes Derrida's Random Energy Model (REM) and Generalized Random Energy Model (GREM) and a nonhierarchical version (BK-GREM) by Bolthausen and Kistler. The limiting free…
We consider the random transverse-field Ising model in $d=3$ dimensions with long-range ferromagnetic interactions which decay as a power $\alpha > d$ with the distance. Using a variant of the strong disorder renormalization group method we…
The spherical spin model with infinite-range ferromagnetic interactions is investigated analytically in the framework of non-extensive thermostatics generalizing the Boltzmann-Gibbs statistical mechanics. We show that for repulsive…
We extend a previously studied lattice model of particles with infinite repulsions to the case of finite energy interactions. The phase diagram is studied using grand canonical Monte Carlo simulation. Simulations of dynamical phenomena are…
We study the extremes of a class of Gaussian fields with in-built hierarchical structure. The number of scales in the underlying trees depends on a parameter alpha in [0,1]: choosing alpha=0 yields the random energy model by Derrida (REM),…
Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence…