Related papers: Phase Transitions in a Network with Assortative Mi…
We find the exact critical temperature $T_c$ of the nearest-neighbor ferromagnetic Ising model on an `equilibrium' random graph with an arbitrary degree distribution $P(k)$. We observe an anomalous behavior of the magnetization, magnetic…
Using previous results from boundary conformal field theory and integrability, a phase diagram is derived for the 2 dimensional Ising model at its bulk tri-critical point as a function of boundary magnetic field and boundary spin-coupling…
This work considers an Ising model on the Apollonian network, where the exchange constant $J_{i,j}\sim1/(k_ik_j)^\mu$ between two neighboring spins $(i,j)$ is a function of the degree $k$ of both spins. Using the exact geometrical…
Coordination processes in complex systems can be related to the problem of collective ordering in networks, many of which have modular organization. Investigating the order-disorder transition for Ising spins on modular random networks,…
We consider the ferromagnetic Ising model on a highly inhomogeneous network created by a growth process. We find that the phase transition in this system is characterised by the Berezinskii--Kosterlitz--Thouless singularity, although…
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…
The Ising model in clustered scale-free networks has been studied by Monte Carlo simulations. These networks are characterized by a degree distribution of the form P(k) ~ k^(-gamma) for large k. Clustering is introduced in the networks by…
The dynamical response of an Ising ferromagnet to a plane polarised standing magnetic field wave is modelled and studied here by Monte Carlo simulation in two dimensions. The amplitude of standing magnetic wave is modulated along the…
A new type of collective excitations, due exclusively to the topology of a complex random network that can be characterized by a fractal dimension $D_F$, is investigated. We show analytically that these excitations generate phase…
Phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a…
The purpose of this article is to present a detailed numerical study of the second-order phase transition in the 2D Ising model. The importance of correctly presenting elementary theory of phase transitions, computational algorithms and…
We consider a one-dimensional Ising model in a transverse magnetic field coupled to a dissipative heat bath. The phase diagram and the critical exponents are determined from extensive Monte Carlo simulations. It is shown that the character…
In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the…
The two dimensional ferromagnetic Ising model in the presence of a propagating magnetic field wave (with well defined frequency and wavelength) is studied by Mone Carlo simulation. This study differs from all of the earlier studies done so…
We propose a degree-based coarse graining approach that not just accelerates the evaluation of dynamics on complex networks, but also satisfies the consistency conditions for both equilibrium statistical distributions and nonequilibrium…
We explore the phase diagram of Ising spins on one-dimensional chains which criss-cross in two perpendicular directions and which are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum…
This chapter provides a general introduction of network modeling in psychometrics. The chapter starts with an introduction to the statistical model formulation of pairwise Markov random fields (PMRF), followed by an introduction of the PMRF…
We investigate the efficient learning of magnetic phases using artificial neural networks trained on synthetic data, combining computational simplicity with physics-informed strategies. Focusing on the diluted Ising model, which lacks an…
We study the surface phase diagram of the three-dimensional kinetic Ising model below the equilibrium critical point subjected to a periodically oscillating magnetic field. Changing the surface interaction strength as well as the period of…
The antiferromagnetic quantum Ising chain has a quantum critical point which belongs to the universality class of the transverse Ising model (TIM). When a longitudinal field ($h$) is switched on, the phase transition is preserved, which…