Related papers: Random Energy Model with complex replica number, c…
Using the newly introduced theory of finite-temperature reduced density matrix functional theory, we apply the first-order approximation to the homogeneous electron gas. We consider both collinear spin states as well as symmetry broken…
Modern experiments aimed at measuring neutrino oscillation parameters have entered the age of precision. The determination of these parameters strongly depends on the ability to reconstruct the energy distributions of the neutrino beams. We…
We study the statistics of thermodynamic quantities in two related systems with quenched disorder: A (1+1)-dimensional planar lattice of elastic lines in a random potential and the 2-dimensional random bond dimer model. The first system is…
We explore the application of approximation schemes from many body physics, including the Hartree-Fock method and random phase approximation (RPA), to the problem of analyzing the low energy excitations of a polymer chain made up of bosonic…
In this article, we review existing probabilistic models for modeling abundance of fixed-length strings (k-mers) in DNA sequencing data. These models capture dependence of the abundance on various phenomena, such as the size and repeat…
Studies of the ultrarelativistic collisions of hadrons and nuclei at different centrality and energy enable to explore the QCD phase diagram in a wide range of temperature and baryon density. Long-range correlation studies are considered as…
Transverse momentum spectra of the reaction products from proton-proton and nucleus-nucleus collisions are discussed within the phenomenological frameworks of statistical phase-space and string fragmentation models. It will be shown that a…
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…
Modellers of complex biological or social systems are often faced with an invidious choice: to use simple models with few mechanisms that can be fully analysed, or to construct complicated models that include all the features which are…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
In this paper the phase structure of the massive $\lambda \phi^4$ model at finite temperature ($T \neq 0$) is investigated by applying a resummation method inspired by the renormalization-group (RG) improvement to the one-loop effective…
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…
The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables…
We introduce a novel class of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) paradigm, called Residual Reservoir Memory Networks (ResRMNs). ResRMN combines a linear memory reservoir with a non-linear…
We derive the spectral properties of adjacency matrix of complex networks and of their Laplacian by the replica method combined with a dynamical population algorithm. By assuming the order parameter to be a product of Gaussian…
An expression for the electromagnetic field energy density in a dispersive, lossy, left-handed metamaterial, consisting of an array of split-ring resonators and an array of wires is derived. An electromagnetic field with general…
We study the localization in the one-dimensional trap model in terms of statistical mechanics of trajectories. By numerically investigating overlap between trajectories of two particles on a common disordered potential, we find that there…
Energy-Based Models have emerged as a powerful framework in the realm of generative modeling, offering a unique perspective that aligns closely with principles of statistical mechanics. This review aims to provide physicists with a…
The string-net model describes a vast family of topological orders in two spatial dimensions. Here, we consider the effect of thermal fluctuations on these topological phases. In the original string-net model, the description of charge…
Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general…