Related papers: Integrability Condition in the Statistical Model a…
In this paper, we consider Ising models with ferromagnetic pair interactions. We prove that the Ursell functions $u_{2k}$ satisfy: $(-1)^{k-1}u_{2k}$ is increasing in each interaction. As an application, we prove a 1983 conjecture by…
We introduce an integrable stochastic process associated with the $D_2$ quantum group, which can be decomposed into two symmetric simple exclusion processes. We establish the integrability of the model under three types of boundary…
The Ising model is well-known for illustrating the fundamental characteristics of phase transitions in closed systems. In this article, we propose a generalization of the two-dimensional Ising model to open systems, considering the…
Input-to-state stability (ISS) and $\mathcal{L}_2$-gain are well-known robust stability properties that continue to find wide application in the analysis and control of nonlinear dynamical systems and their interconnections. We investigate…
An inflation model with inverse symmetry breaking of two scalar fields is proposed. Constraints on the parameters for a successful inflation are obtained. In general the inequality $\lambda_1\ll g <\lambda_2$ should be satisfied, where…
Elliptic and parabolic integro-differential model problems are considered in the whole space. By verifying H\"ormander condition, the existence and uniqueness is proved in L_{p}-spaces of functions whose regularity is defined by a scalable,…
The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager's work of the forties,…
We classify integrable Hamiltonian equations in 3D with the Hamiltonian operator d/dx, where the Hamiltonian density h(u, w) is a function of two variables: dependent variable u and the non-locality w such that w_x=u_y. Based on the method…
We present a one-loop calculation of the static potential in the SU(2)-Higgs model. The connection to the coupling constant definition used in lattice simulations is clarified. The consequences in comparing lattice simulations and…
In some higher dimensional nonlinear field theories integrable subsectors with infinitely many conservation laws have been identified by imposing additional integrability conditions. Originally, the complex eikonal equation was chosen as…
The partition function of the 2D Ising model coupled to an external magnetic field is studied. We show that the sum over the spin variables can be reduced to an integration over a finite number of variables. This integration must be…
We consider the Euler type integral associated to the configuration space of points on an elliptic curve, which is an analogue of the hypergeometric function associated to the configuration space of points on a projective line. We calculate…
The method of exhaustion is generalized to a simple formula that can be used to integrate functions under very general conditions, provided that the integral exists. Both a geometric proof (following the usual procedure for the method of…
Using Monte Carlo simulations we study the two-dimensional Ising model on triangular, square, and hexagonal lattices with various topologies. We focus on the behavior of the magnetic susceptibility and of the specific heat near the critical…
The authors establish the necessary and sufficient conditions under which certain combinations of Gaussian hypergeometric function and elementary function are monotone in the parameter, which generalize the recent results of generalized…
We establish a criterion for when an abelian extension of infinite-dimensional Lie algebras integrates to a corresponding Lie group extension $\hat{G}$ of $G$ by $A$, where $G$ is a connected, simply connected Lie group and $A$ is a…
We consider bosonized $QCD_2$, and prove that after rewritting the theory in terms of gauge invariant fields, there exists an integrability condition valid for the quantum theory as well. Furthermore, performing a duality type…
We demonstrate that the necessary condition for $SO(N) \times SO(N)$ duality invariance manifests as a partial differential equation in two-dimensional scalar theories. This condition, expressed as a partial differential equation,…
We prove a meromorphic integrability condition at order 2 near a homothetic orbit for a meromorphic homogeneous potential of degree -1, which extend the Morales Ramis conditions of order 1. Conversely, we prove that if this criterion is…
The geometric theory of Lie systems is used to establish integrability conditions for several systems of differential equations, in particular some Riccati equations and Ermakov systems. Many different integrability criteria in the…