Related papers: Replica solution of the Random Energy Model
We solve the random energy model when the energies of the configurations take only integer values. In the thermodynamic limit, the average overlaps remain size dependent and oscillate as the system size increases. While the extensive part…
In this note we introduce a method to calculate the finite volume corrections to the mean field results for the free energy when replica symmetry is broken at one-step. We find that the naive results are modified by the presence of…
We review uses of the generalized-ensemble algorithms for free-energy calculations in protein folding. Two of the well-known methods are multicanonical algorithm and replica-exchange method; the latter is also referred to as parallel…
We discuss the use of the replica ansatz in computing free energies in random matrix theory, and confirm a conjectured condition on analytic continuation in the replica index at large-N.
We provide an exact expression of the moment of the partition function for random energy models of finite system size, generalizing an earlier expression for a grand canonical version of the discrete random energy model presented by the…
We have developed a new simulation algorithm for free-energy calculations. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temperatures are exchanged during the simulation in…
While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium…
A systematic replica field theory calculations are analysed using the examples of two particular one-dimensional "toy" random models with Gaussian disorder. Due to apparent simplicity of the model the replica trick calculations can be…
We discuss resummation strategies for free energy in quantum field theories at nonzero temperatures T. We point out that resummations should be performed for the short- and long-distance parts separately in order to avoid spurious…
In this paper we present the exact solution for the average minimum energy of the random bipartite matching model with an arbitrary finite number of elements where random paired interactions are described by independent exponential…
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 replica analytic continuation using several simple models in order to prove mathematically the validity of replica analysis, which is used in a wide range of fields related to large scale complex systems. While replica analysis…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
Calculating free energy differences is a topic of substantial interest and has many applications including molecular docking and hydration, solvation, and binding free energies which is used in computational drug discovery. However, in…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
A non-iterative method of reconstruction is proposed from data of MRI system and of a harmonic electro-magnetic field at Larmor frequency. The method is based on the exact analytic formula for the contrast source function. A geometric…
We discuss the ways of extracting a low energy scale of an underlying theory using high energy scattering data. Within an exactly solvable model of quantum mechanics we analyze a technique based on introduction of nonperturbative power…
By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via…
We compute the free energy at all temperatures for the spherical pure $p$-spin models from the generalized Thouless-Anderson-Palmer representation. This is the first example of a mixed $p$-spin model for which the free energy is computed in…
An expression for the moment of partition function valid for any finite system size $N$ and complex power $n (\Re(n)>0)$ is obtained for a simple spin glass model termed the {\em discrete random energy model} (DREM). We investigate the…