Related papers: The work of Hugo Duminil-Copin
In the past 30 years there have been extensive discoveries in the theory of integrable statistical mechanical models including the discovery of non-linear differential equations for Ising model correlation functions, the theory of random…
We present a new $(2+1)$-dimensional field theory showing exotic statistics and fractional spin. This theory is achieved through a redefinition of the gauge field $A_{\mu}$. New properties are found. Another way to implement the field…
This is a survey article dedicated to the study of topological quantities in theory of normal metals discovered in the works of the authors during the last years. Our results are based on the theory of dynamical systems on Fermi surfaces.…
In these notes, the application of Feynman's sum-over-paths approach to thermal phase transitions is discussed. The paradigm of such a spacetime approach to critical phenomena is provided by the high-temperature expansion of spin models.…
This is my laudation for Scholze's Fields medal 2018.
The Nobel Prize in Physics 2025 has been awarded to John Clarke, John Martinis, and Michel Devoret for "the discovery of macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit". The paper explains the…
We develop a descriptive account of scientific reward in physics based on the concept of the time-dependent Polydoxon, defined as the structured set of empirically viable theories at a given time. We argue that highly rewarded…
This article is written in memory of Pierre Hohenberg with appreciation for his deep commitment to the basic principles of theoretical physics. I summarize recent developments in the theory of dislocation-enabled deformation of crystalline…
The Dumont differential system on the Jacobi elliptic functions was introduced by Dumont (Math Comp, 1979, 33: 1293--1297) and was extensively studied by Dumont, Viennot, Flajolet and so on. In this paper, we first present a labeling scheme…
Despite its amazing quantitative successes and contributions to revolutionary technologies, physics currently faces many unsolved mysteries ranging from the meaning of quantum mechanics to the nature of the dark energy that will determine…
It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way,…
We put forward several information-theoretic measures for analyzing the uncertainty of fermionic phase-space distributions using the theory of supernumbers. In contrast to the bosonic case, the anticommuting nature of Grassmann variables…
Deformation of Ising Hamiltonian by means of replacing a site spin $s_i$ by $s_i^q$ and statistics generalization with help of the substituting deformed probability $p_i^q$ instead of $p_i$ are studied jointly within mean--field scheme.…
This paper describes some strategies used in a `transition' course. Such courses help undergraduate mathematics majors move from learning procedures to learning to function as critical mathematicians in order to understand and work with…
We study a phase transition in a 3D lattice gauge theory, a "coarse-grained" version of a classical dimer model. Duality arguments indicate that the dimer lattice theory should be dual to a XY model coupled to a gauge field with geometric…
The process of phase separation of binary systems is described by the Cahn-Hilliard equation. The main objective of this article is to give a classification on the dynamic phase transitions for binary systems using either the classical…
Much work has been devoted to analysing thermodynamic models for solid dispersions with a view to identifying regions in the phase diagram where amorphous phase separation or drug recrystallization can occur. However, detailed partial…
Without attempting to summarize the vast field of statistical mechanics, we briefly mention some of the progress that was made in areas which have enjoyed Barry Simon's interests. In particular, we focus on rigorous non-perturbative results…
This is an extended version of my Nobel Lecture, delivered on December $8^{th}$ 2021. I will recall the genesis of the concept of multiple equilibria in natural sciences. I will then describe my contribution to the development of this…
In the present paper we present results of calculations obtained with the use of the theoretical method described in our preceding paper [1] and perform detail analysis of alpha helix-random coil transition in alanine polypeptides of…