Related papers: Exploring the variational method for thermodynamic…
Using the formalism of differential equations, we introduce a new method to continuously deform the $s$-embeddings associated with a family of Ising models as their coupling constants vary. This provides a geometric interpretation of the…
Machine learning has become a central technique for modeling in science and engineering, either complementing or as surrogates to physics-based models. Significant efforts have recently been devoted to models capable of predicting field…
An analysis is made of various methods of phenomenological renormalization based on finite-size scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made…
Machine learning for phase transition has received intensive research interest in recent years. However, its application in percolation still remains challenging. We propose an auxiliary Ising mapping method for machine learning study of…
The thermal dynamics in thermo-mechanical systems exhibits a much slower time scale compared to the structural dynamics. In this work, we use the method of multiple scales to reduce the thermo-mechanical structural models with a…
The 3D Ising-like system in the external field is described using the non-perturbative collective variables method. The universal as well as nonuniversal system characteristics are obtained within the framework of this approach. The…
We provide non-asymptotic $L^1$ bounds to the normal for four well-known models in statistical physics and particle systems in $\mathbb{Z}^d$; the ferromagnetic nearest-neighbor Ising model, the supercritical bond percolation model, the…
We enlighten some critical aspects of the three-dimensional ($d=3$) random-field Ising model from simulations performed at zero temperature. We consider two different, in terms of the field distribution, versions of model, namely a Gaussian…
By means of the principle of minimal sensitivity we generalize the microcanonical inflection-point analysis method by probing derivatives of the microcanonical entropy for signals of transitions in complex systems. A strategy of…
Thermodynamics with internal variables is a common approach in continuum mechanics to model inelastic (i.e., non-equilibrium) material behavior. While this approach is computationally and theoretically attractive, it currently lacks a…
In order to find reliable and efficient numerical approximation schemes, we suggest to identify the Functional Renormalization Group flow equations of one-particle irreducible two-point functions as Hamilton-Jacobi(-Bellman)-type partial…
This is an introduction to conformal invariance and two-dimensional critical phenomena for graduate students and condensed-matter physicists. After explaining the algebraic foundations of conformal invariance, numerical methods and their…
We develop further the study of a system in contact with a multibath having different temperatures at widely separated timescales. We consider those systems that do not thermalize in finite times when in contact with an ordinary bath but…
Percolation in a scale-free hierarchical network is solved exactly by renormalization-group theory, in terms of the different probabilities of short-range and long-range bonds. A phase of critical percolation, with algebraic…
Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high temperature region and coexistence of at least two Gibbs…
We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
The percolation study offers valuable insights into the characteristics of phase transition, shedding light on the underlying mechanisms that govern the formation of global connectivity within the system. We explore the percolation phase…
This paper introduces variational design methods that are novel to Geophysics, and discusses their benefits and limitations in the context of geophysical applications and more established design methods. Variational methods rely on…
Inverse problems are of great importance in astrophysics for deriving information about the physical characteristics of hot optically thin plasma sources from their EUV and X-ray spectra. We describe and test an iterative method developed…