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We give a short non-technical introduction to the Ising model, and review some successes as well as challenges which have emerged from its study in probability and mathematical physics. This includes the infinite-volume theory of phase…

Dry active matter in an anisotropic medium is of experimental relevance, and the interplay between anisotropy and the dynamics of the active matter remains under-explored. Here, we derive the hydrodynamic equations of a generic dry polar…

The mechanical response of solids depends on temperature because the way atoms and molecules respond collectively to deformation is affected at various levels by thermal motion. This is a fundamental problem of solid state science and plays…

We report the new exact results on one of the best studied models in statistical physics: the classical antiferromagnetic Ising chain in a magnetic field. We show that the model possesses an infinite cascade of thermal phase transitions…

An anyon-chain-like lattice model with symmetry described by the Ising fusion category is studied. Combining numerical and analytical studies, we uncover a rich phase diagram that contains three phases: a symmetric critical phase and two…

We study a continuous quantum phase transition that breaks a $Z_2$ symmetry. We show that the transition is described by a new critical point which does not belong to the Ising universality class, despite the presence of well defined…

We show that resonance phenomena can be treated as nonequilibrium phase transitions. Resonance phenomena, similar to equilibrium phase transitions, are accompanied by some kind of symmetry breaking and can be characterized by order…

Dynamics of Ising models is a much studied phenomenon and has emerged as a rich field of present-day research. An important dynamical feature commonly studied is the quenching phenomenon below the critical temperature. In this thesis we…

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…

This note introduces the double flip move for accelerating the Swendsen-Wang algorithm for Ising models with mixed boundary conditions below the critical temperature. The double flip move consists of a geometric flip of the spin lattice…

The $2$d orders are a sub class of causal sets, which is especially amenable to computer simulations. Past work has shown that the $2$d orders have a first order phase transition between a random and a crystalline phase. When coupling the…

In an emergency situation, imitation of strategies of neighbours can lead to an order-disorder phase transition, where spatial clusters of pedestrians adopt the same strategy. We assume that there are two strategies, cooperating and…

We investigate the quantum dynamics of many-body systems subject to local, i.e. restricted to a limited space region, time-dependent perturbations. If the perturbation drives the system across a quantum transition, an off-equilibrium…

We develop a fully microscopic, statistical mechanics approach to study phase transitions in Ising systems with competing interactions at different scales. Our aim is to consider orientational and positional order parameters in a unified…

Microscopic mechanisms of natural processes are frequently understood in terms of random walk models by analyzing local particle transitions. This is because these models properly account for dynamic processes at the molecular level and…

Coarsening dynamics, the canonical theory of phase ordering following a quench across a symmetry breaking phase transition, is thought to be driven by the annihilation of topological defects. Here we show that this understanding is…

We assume that, in equilibrium, nuclear matter at reduced density and moderate finite temperature, breaks up into many fragments. A strong support to this assumption is provided by date accumulated from intermediate energy heavy ion…

There are deep analogies between the melting dynamics in systems with a first order phase transition and the dynamics from equilibrium in super-cooled liquids. For a class of Ising spin models undergoing a first order transition - namely…

The simplified model of first-order transition in a media with frozen long-range transition-temperature disorder is considered. It exhibits the smearing of the transition due to appearance of the intermediate inhomogeneous phase with…

Effects of the averaging over disorder realizations (samples) on the phase behavior are analyzed in terms of the mean field approximation for the random field Ising model with infinite range interactions. It is found that the averaging is…