Related papers: Replica method and finite volume corrections
We present a systematic and exact way of computing finite size corrections for the random energy model, in its low temperature phase. We obtain explicit (though complicated) expressions for the finite size corrections of the overlap…
We investigate the effects of finite size corrections on the overlap probabilities in the Generalized Random Energy Model (GREM) in two situations where replica symmetry is broken in the thermodynamic limit. Our calculations do not use…
The replica method for a quenched disordered system is considered in a perturbative field theory. Since correction in a finite-order perturbation is given in a polynomial of the replica number $n$, the zero-replica limit $n \to 0$ is…
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…
The alternative replica technique which involve summation over all integer momenta of the partition function and which does not require analytic continuation to non-integer values of the replica parameter $n$ is discussed. In terms of this…
The presence of a random magnetic field in ferromagnetic systems leads, in the broken phase, to an anomalous $O(\sqrt{1/N})$ convergence of some thermodynamic quantities to their asymptotic limits. Here we show a general method, based on…
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 study the statistical mechanics of a model describing the coevolution of species interacting in a random way. We find that at high competition replica symmetry is broken. We solve the model in the approximation of one step replica…
Centered finite volume methods are considered in the context of Numerical Relativity. A specific formulation is presented, in which third-order space accuracy is reached by using a piecewise-linear reconstruction. This formulation can be…
In this talk I will presente the physical meaning of replica symmetry breaking stressing the physical concepts. After introducing the theoretical framework and the experimental evidence for replica symmetry breaking, I will describe some of…
We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any…
In this paper we calculate the full one-loop finite volume corrections to the quantities $< x >_{u\pm d}$ within the framework of two-flavor baryon chiral perturbation theory and show estimates of these effects for the leading one-loop…
We develop an unambiguous and practical method to calculate one-loop quantum corrections to the energies of classical time-independent field configurations in renormalizable field theories. We show that the standard perturbative…
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…
We develop a new method to calculate finite size corrections for form factors in two-dimensional integrable quantum field theories. We extract these corrections from the excited state expectation value of bilocal operators in the limit when…
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 apply the resummed version of the L\"uscher formula to analyze finite volume corrections to the mass of the nucleon and of heavy mesons. We show that by applying the subthreshold expansion of the scattering amplitudes one can express the…
Replica symmetry breaking solutions for the new replica anzats, related to general ultrametric spaces, are investigated. A variant of analysis on trees is developed and applied to the computation of the n\to0 limit in the new replica…
We numerically implement the variational approach for reconstruction in the inverse crack and cavity problems developed by one of the authors. The method is based on a suitably adapted free-discontinuity problem. Its main features are the…
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…