Related papers: Partition function for several Ising model interfa…
The path integral approach offers not only an exact expression for the non- equilibrium dynamics of dissipative quantum systems, but is also a convenient starting point for perturbative treatments. An alternative way to explore the…
The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the maximum of the finite number of continuously differentiable (in…
We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with…
We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free…
We obtain the diagonal reflection matrices for a recently introduced family of dilute ${\rm A}_L$ lattice models in which the ${\rm A}_3$ model can be viewed as an Ising model in a magnetic field. We calculate the surface free energy from…
In order to elucidate the important characteristics of hysteretic response, such as types of the frequency dispersion curves, the decay of hysteresis loop area, the mechanism of domain nucleation and/or growth in the dynamic process, etc.,…
Employing the exact solution of Onsager for two-dimensional Ising models, simple expressions are proposed for computing the partition function, magnetization, specific heat and susceptibility for non-zero magnetic fields of square lattices.…
Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal…
We present detailed analytical calculations for an 1D Ising ring of arbitrary number of spin-1/2 particles, in order to reveal entanglement properties of the stationary states. We show that the ground state and specific eigenstates of the…
In this paper we design an iterative domain decomposition method for free boundary problems with nonlinear flux jump condition. Our approach is related to damped Newton's methods. The proposed scheme requires, in each iteration, the…
Gradient descent dynamics in complex energy landscapes, i.e. featuring multiple minima, finds application in many different problems, from soft matter to machine learning. Here, we analyze one of the simplest examples, namely that of soft…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
We suggest a generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the…
In 1944 Onsager published the formula for the partition function of the Ising model for the infinite square lattice. He was able to express the internal energy in terms of a special function, but he left the free energy as a definite…
We propose a way to analyze the landscape geometry explored by a glassy system after a quench solely based on time series of energy values recorded during a simulation. Entry and exit times for landscape `valleys' are defined operationally…
We consider the three-dimensional Ising model slightly below its critical temperature, with boundary conditions leading to the presence of an interface. We show how the interfacial properties can be deduced starting from the particle modes…
The replica method has been used to calculate the interface free energy associated with the change from periodic to anti-periodic boundary conditions in finite-dimensional p-spin glass models in the phase which at mean-field level has…
Exploiting stochastic path integral theory, we obtain \emph{by simulation} substantial gains in efficiency for the computation of reaction rates in one-dimensional, bistable, overdamped stochastic systems. Using a well-defined measure of…
Some consequences of the analyticity of the free energy (pressure) of QCD at finite chemical potential are deduced. These include a method for numerical exploration of the full phase diagram by a novel use of simulations at imaginary…
The combined effect of finite potential barriers and dielectric mismatch between dot and matrix on excitonic properties of semiconductor quantum dots has been studied. To avoid the unphysical divergence in the self-polarization energy which…