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Long-range interacting spin systems are ubiquitous in physics and exhibit a variety of ground state disorder-to-order phase transitions. We consider a prototype of infinite-range interacting models known as the Lipkin-Meshkov-Glick (LMG)…
In order to investigate the effects of connectivity and proximity in the specific heat, a special class of exactly solvable planar layered Ising models has been studied in the thermodynamic limit. The Ising models consist of repeated…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
Employing the self-learning quantum Monte Carlo algorithm, we investigate the frustrated transverse-field triangle-lattice Ising model coupled to a Fermi surface. Without fermions, the spin degrees of freedom undergoes a second-order…
Extensive Monte Carlo simulations are employed in order to study the dynamic critical behavior of the one-dimensional Ising magnet, with algebraically decaying long-range interactions of the form $\frac{1}{r^{d+\sigma}}$, with…
Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical…
We demonstrate the presence of an extended critical phase in the transverse field Ising magnet on the triangular lattice, in a regime where both thermal and quantum fluctuations are important. We map out a complete phase diagram by means of…
After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…
The mixed spin-1/2 and spin-S Ising model on the Union Jack (centered square) lattice with four different three-spin (triplet) interactions and the uniaxial single-ion anisotropy is exactly solved by establishing a rigorous mapping…
In this work, we investigate an important class of nonequilibrium dynamics in the form of nonreciprocal interactions. In particular, we study how nonreciprocal coupling between two $O(n_i)$ order parameters (with $i=1,2$) affects the…
We solve a long-standing puzzle in Statistical Mechanics of disordered systems. By performing a high-statistics simulation of the D=3 random-field Ising model at zero temperature for different shapes of the random-field distribution, we…
The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree…
Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a…
Non-equilibrium critical phenomena generally exist in many dynamic systems, like chemical reactions and some driven-dissipative {reactive} particle systems. Here, by using computer simulation and theoretical analysis, we demonstrate the…
We investigate the interaction dependence of the liquid-gas critical point of symmetric nuclear matter in finite-temperature lattice effective field theory. Building on the pinhole-trace algorithm, we benchmark a first-order perturbative…
We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical…
The nonasymptotic critical behavior of sound attenuation coefficient has been studied in an elastically isotropic Ising system above the critical point on the basis of a complete stochastic model including both spin-energy and…
A family of nonequilibrium kinetic Ising models, introduced earlier, evolving under the competing effect of spin flips at {\it zero temperature} and nearest neighbour random spin exchanges is further investigated here. By increasing the…
We study the Ising model on $\mathbb{Z}^{2}$ and show, via numerical simulation, that allowing interactions between spins separated by distances $1$ and $m$ (two ranges), the critical temperature, $ T_c (m) $, converges monotonically to the…
Magnetic thin films and 2D arrays of magnetic nanoparticles exhibit unique physical properties that make them valuable for a wide range of technological applications. In such systems, dipolar interactions play a crucial role in determining…