Related papers: Universality Diagram of Phase Transitions in Long-…
We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics…
We explore the phase diagram of an O(n) model on the honeycomb lattice with vacancies, using finite-size scaling and transfer-matrix methods. We make use of the loop representation of the O(n) model, so that $n$ is not restricted to…
We find a possibility of a weak universality of spin-glass phase transitions in three-dimensional $\pm J$ models. The Ising, the XY and the Heisenberg models seem to undergo finite-temperature phase transitions with a ratio of the critical…
Statistical mechanical models with local interactions in $d>1$ dimension can be regarded as $d=1$ dimensional models with regular long range interactions. In this paper we study the critical properties of Ising models having $V$ sites, each…
The ordering of charges on half-filled hypercubic lattices is investigated numerically, where electroneutrality is ensured by background charges. This system is equivalent to the $s = 1/2$ Ising lattice model with antiferromagnetic $1/r$…
We extend previous results due to Ding and Zhuang in order to prove that a phase transition occurs for the long range Ising model in lower dimensions. By making use of a recent argument due to Affonso, Bissacot and Maia from 2022 which…
Phase transitions and critical phenomena are among the most intriguing phenomena in nature and society. They are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter show marvelous phenomena of scaling…
Order-disorder phase transition of the ferromagnetic Ising model is investigated on a series of two-dimensional lattices that have negative Gaussian curvatures. Exceptional lattice sites of coordination number seven are distributed on the…
We consider the random transverse-field Ising model in $d=3$ dimensions with long-range ferromagnetic interactions which decay as a power $\alpha > d$ with the distance. Using a variant of the strong disorder renormalization group method we…
We review the field theory approach to percolation processes. Specifically, we focus on the so-called simple and general epidemic processes that display continuous non-equilibrium active to absorbing state phase transitions whose asymptotic…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
The deconfinement transition in SU(2) gauge theory and the magnetization transition in the Ising model belong to the same universality class. The critical behaviour of the Ising model can be characterized either as spontaneous breaking of…
This is a (long) survey about applications of percolation theory in equilibrium statistical mechanics. The chapters are as follows: 1. Introduction 2. Equilibrium phases 3. Some models 4. Coupling and stochastic domination 5. Percolation 6.…
The behavior of many magnetic and dielectric solids, and the more contemporary magnetic super-lattices, is governed by dipolar interactions. They are anisotropic and long-ranged, having varied consequences ranging from ground states with…
A detailed investigation of the scaling properties of the fully finite ${\cal O}(n)$ systems with long-range interaction, decaying algebraically with the interparticle distance $r$ like $r^{-d-\sigma}$, below their upper critical dimension…
It has been well established that spatially extended, bistable systems that are driven by an oscillating field exhibit a nonequilibrium dynamic phase transition (DPT). The DPT occurs when the field frequency is on the order of the inverse…
The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager's work of the forties,…
Jamming and percolation transitions in the standard random sequential adsorption of particles on regular lattices are characterized by a universal set of critical exponents. The universality class is preserved even in the presence of…
A cluster weight Ising model is proposed by introducing an additional cluster weight in the partition function of the traditional Ising model. It is equivalent to the O($n$) loop model or $n$-component face cubic loop model on the…
Phase transitions to absorbing states are among the simplest examples of critical phenomena out of equilibrium. The characteristic feature of these models is the presence of a fluctuationless configuration which the dynamics cannot leave,…