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We study the 3D Ising model in the infinite volume limit $N_{x,y,z}\to\infty$ by means of numerical simulations. We determine $T_c$ as well as the critical exponents $\beta,\gamma$ and $\nu$, based on finite-size scaling and histogram…
A periodic Ising model is one endowed with interactions that are invariant under translations of members of a full-rank sublattice $\mathfrak{L}$ of $\mathbb{Z}^2$. We give an exact, quantitative description of the critical temperature,…
Equilibrium and nonequilibrium systems exhibit power-law singularities close to their critical and bifurcation points respectively. A recent study has shown that biochemical nonequilibrium models with positive feedback belong to the…
Conformal transformations can be used to obtain the order parameter for two-dimensional systems at criticality in finite geometries with fixed boundary conditions on a connected boundary. To the known examples of this class (such as the…
Magnetization isotherms of the 5f-electron ferromagnets URhGa, UCoGa and UCo0.98Ru0.02Al were measured at temperatures in the vicinity of their Curie temperature in order to investigate the critical behavior near the ferromagnetic phase…
The finite size analysis of the nonequilibrium phase transition, in two dimensional Ising ferromagnet driven by plane propagating magneticwave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium…
The asymptotic behaviour near phase transitions can be suitably characterized by the scaling of $\Delta s/Q^2$ with $\epsilon=1-T/T_c$, where $\Delta s$ is the excess entropy and $Q$ is the order parameter. As $\Delta s$ is obtained by…
We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size which is typical of critical phenomena. Our approach is to introduce an external,…
We use a non-equilibrium simulation method to study the spin glass transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity $v$ (temperature change versus time) in Monte Carlo…
To provide an understanding of the universal thermodynamic properties of cuprate superconductors, emerging from the empirical correlations and phase diagrams, we analyze them in terms of the scaling theory of finite temperature and quantum…
We study the critical exponents in the universal scaling laws of a holographic non-equilibrium steady state nearby its critical point of phase transition, which is driven by an AC electric field sitting in the boundary of the bulk. The…
We study incompressible systems of motile particles with alignment interactions. Unlike their compressible counterparts, in which the order-disorder (i.e., moving to static) transition, tuned by either noise or number density, is…
The well known scaling laws relating critical exponents in a second order phase transition have been generalized to the case of an arbitrarily higher order phase transition. In a higher order transition, such as one suggested for the…
We consider a new class of unconventional critical phenomena that is characterized by singularities only in dynamical quantities and has no thermodynamic signatures. A possible example is the recently proposed many-body localization…
We study the Ising model with an external magnetic field on random tetravalent planar maps and investigate its critical behavior. Explicit expressions for spontaneous magnetization and the susceptibility are computed and the critical…
The behavior of fluids in the vicinity of the liquid-gas critical point is studied within the cell fluid model framework. The analytic method for deriving the equation of state of a cell fluid model in the low-temperature region (T<Tc) is…
The ferromagnet-to-paramagnet transition of the four-dimensional random-field Ising model with Gaussian distribution of the random fields is studied. Exact ground states of systems with sizes up to 32^4 are obtained using graph theoretical…
We consider the real $\beta$-ensemble (or 1D log-gas) of dimension $N$ in the high-temperature regime, \textit{i.e.} where the inverse temperature $\beta$ scales as $N\beta=2P$ with $P$ a fixed positive parameter. We establish the large-$N$…
Among the statistical mechanical frameworks able to describe systems in non-equilibrium steady states such as collisionless plasmas, self-gravitating systems and other complex systems, superstatistics have gained recent attention.…
Based on the foundations of thermodynamics and the equilibrium conditions for the coexistence of two phases in a magnetic Ising-like system, we show, first, that there is a critical point where the isothermal susceptibility diverges and the…