Related papers: Replica solution of the Random Energy Model
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…
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise…
The distribution function of the free energy fluctuations in one-dimensional directed polymers with free boundary conditions is derived by mapping the replicated problem to the N-particle quantum boson system with attractive interactions.…
Alternative forms of the solutions to the quantum field equations and their implications for physical theory are considered. Incorporation of these alternative solution forms, herein deemed "supplemental solutions", into the development of…
We develop randomized matrix-free algorithms for estimating partial traces, a generalization of the trace arising in quantum physics and chemistry. Our algorithm improves on the typicality-based approach used in [T. Chen and Y-C. Cheng,…
This paper introduces a novel approach to address inherent limitations in the Residual Power Series (RPS) method and its variants with Laplace-like transforms when applied to solving time-fractional differential equations. Existing methods,…
For problems in astrophysics, planetary science and beyond, numerical simulations are often limited to simulating fewer particles than in the real system. To model collisions, the simulated particles (aka superparticles) need to be inflated…
A well-known result from Hardy and Ramanujan gives an asymptotic expression for the number of possible ways to express an integer as the sum of smaller integers. In this vein, we consider the general partitioning problem of writing an…
A Gaussian variational approximation is often used to study interfaces in random media. By considering the 1+1 dimensional directed polymer in a random medium, it is shown here that the variational Ansatz typically leads to a negative…
We provide an algorithm for generation of momenta (or energies) of relativistic particles according to the relativistic Bose-Einstein or Fermi-Dirac distributions. The algorithm uses rejection method with effectively selected comparison…
A central endeavor of thermodynamics is the measurement of free energy changes. Regrettably, although we can measure the free energy of a system in thermodynamic equilibrium, typically all we can say about the free energy of a…
Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…
We develop a scheme to exactly evaluate the correlation energy in the random-phase approximation, based on linear response theory. It is demonstrated that our formula is completely equivalent to a contour integral representation recently…
Starting with a general discussion, a program is sketched for a quantization based on dilations. This resolving-power quantization is simplest for scalar field theories. The hope is to find a way to relax the requirement of locality so that…
We develop a systematic procedure to approximate generalized free energy in out of equilibrium stochastic systems. The procedure only requires knowledge of the averages of macroscopic observables and uses quasi-equilibrium distribution to…
This paper shows a simple parameter substitution, which makes use of the reciprocal relation of typical objective functions with typical random parameters. Thereby, the accuracy of first-order probabilistic analysis improves significantly…
A common approach to analyze count time series is to fit models based on random sum operators. As an alternative, this paper introduces time series models based on a random multiplication operator, which is simply the multiplication of a…
For a 2-dimensional freely jointed chain with 3 particles and a related model, the average and variance of the kinetic energies of each particle in thermal equilibrium are exactly obtained. The same is done for a related model. The excess…
A vast array of phenomena, ranging from chemical reactions to phase transformations, are analysed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used,…
We propose a replica-exchange method (REM) which does not use pseudo random numbers. For this purpose, we first give a conditional probability for Gibbs sampling replica-exchange method (GSREM) based on the heat bath method. In GSREM,…