Related papers: Kac-Ward solution of the 2D classical and 1D quant…
We derived the thermodynamic curvature of the Ising model on a kagome lattice under the presence of an external magnetic field. The curvature was found to have a singularity at the critical point. We focused on the zero field case to derive…
We study an array of coupled optical cavities in presence of two-photon driving and dissipation. The system displays a critical behavior similar to that of a quantum Ising model at finite temperature. Using the corner-space renormalization…
A nonuniform extension of the Glauber model on a one-dimensional lattice with boundaries is investigated. Based on detailed balance, reaction rates are proposed for the system. The static behavior of the system is investigated. It is shown…
The critical Ising model in two dimensions with a defect line is analyzed to deliver the first exact solution with twisted boundary conditions. We derive exact expressions for the eigenvalues of the transfer matrix and obtain analytically…
We investigate relaxation dynamics along the entire first-order phase transition line by analyzing the time evolution of the free energy landscape in the three-dimensional kinetic Ising model. Near the critical temperature $T_{\rm c}$, the…
The critical behavior of a 3D Ising-like system is studied at the microscopic level of consideration. The free energy of ordering is calculated analytically as an explicit function of temperature, an external field and the initial…
With an auxiliary weak external magnetic field, we reexamine the fundamental thermodynamic function, Gibbs free energy F(T, h), to study the phase transitions in the classical spin lattice models. A cross derivative, i.e. the second-order…
The value of the internal energy per spin is independent of the strip width for a certain class of spin systems on two dimensional infinite strips. It is verified that the Ising model on the kagome lattice belongs to this class through an…
This review provides a brief and quick introduction to the quantum Langevin equation for an oscillator, while focusing on the steady-state thermodynamic aspects. A derivation of the quantum Langevin equation is carefully outlined based on…
We derive an extended lattice gauge theory type action for quantum dimer models and relate it to the height representations of these systems. We examine the system in two and three dimensions and analyze the phase structure in terms of…
We consider high-temperature expansions for the free energy of zero-field Ising models on planar quasiperiodic graphs. For the Penrose and the octagonal Ammann-Beenker tiling, we compute the expansion coefficients up to 18th order. As a…
Many electronic systems exhibit striking features in their dynamical response over a prominent range of experimental parameters. While there are empirical suggestions of particular increasing length scales that accompany such transitions,…
The three-dimensional (3D) Ising model is mapped into a 3D spinless fermionic model by the Jordan-Wigner transformation. The exact solution of the 3D model for spinless fermions is derived analytically by performing a diagonalization…
Conditional probability distributions describe the effect of learning an initially unknown classical state through Bayesian inference. Here we demonstrate the existence of a \textit{learning transition}, having signatures in the long…
The Ising model in small-world networks generated from two- and three-dimensional regular lattices has been studied. Monte Carlo simulations were carried out to characterize the ferromagnetic transition appearing in these systems. In the…
Scaling expressions for the free energy are derived, using the Luttinger-Ward (LW) functional approach in the Eliashberg framework, for two different models of quantum critical point (QCP). First, we consider the spin-density-wave (SDW)…
We study quantum annealing in the quantum Ising model coupled to a thermal environment. When the speed of quantum annealing is sufficiently slow, the system evolves following the instantaneous thermal equilibrium. This quasistatic and…
We investigate the longstanding problem of thermalization of quantum systems coupled to an environment by focusing on a bistable quartic oscillator interacting with a finite number of harmonic oscillators. In order to overcome the…
We consider a spin model, composed of a single spin, connected to an infinitely coordinated Ising chain. Theoretical models of this type arise in various fields of theoretical physics, such as theory of open systems, quantum control and…
In our earlier work [M. Hafez, {\em et al.}, Phys. Lett. A {\bf 373} (2009) 4479] we employed the flow equation method to obtain a classic effective model from a quantum mechanical parent Hamiltonian called, the ionic Hubbard model (IHM).…