The fcc spin-1 Ising (BEG) model has a dense ferromagnetic ($df$) ground state instead of the ferromagnetic ground state at low temperature region and exhibits the dense ferromagnetic ($df$) - ferromagnetic ($F$) phase transition for $d=D/J=2.9$, $k=K/J=-0.5$, $\ell =L/J=0$ and $h=H/J=0$. The critical behavior of the dense ferromagnetic ($df$) - ferromagnetic ($F$) phase transition has been investigated using the cellular automaton cooling and heating algorithms. The universality class and the type of the dense ferromagnetic ($df$) - ferromagnetic ($F$) phase transition have been researched within the framework of the finite - size scaling, the power law relations and the probability distribution. The results show that the dense ferromagnetic- ferromagnetic phase transition is of the second order and the model shows universal second order Ising critical behavior at $d=2.9$ parameter value through $k=-0.5$ line.
In a recent Letter [T.~Dornheim \emph{et al.}, Phys.~Rev.~Lett.~\textbf{125}, 085001 (2020)], we have presented the first \emph{ab initio} results for the nonlinear density response of electrons in the warm dense matter regime. In the present work, we extend these efforts by carrying out extensive new path integral Monte Carlo (PIMC) simulations of a \emph{ferromagnetic} electron gas that is subject to an external harmonic perturbation. This allows us to unambiguously quantify the impact of spin-effects on the nonlinear density response of the warm dense electron gas. In addition to their util…
The $q$-neighbor Ising model is investigated on homogeneous random graphs with a fraction of edges associated randomly with antiferromagnetic exchange integrals and the remaining edges with ferromagnetic ones. It is a nonequilibrium model for the opinion formation in which the agents, represented by two-state spins, change their opinions according to a Metropolis-like algorithm taking into account interactions with only a randomly chosen subset of their $q$ neighbors. Depending on the model parameters in Monte Carlo simulations phase diagrams are observed with first-order ferromagmetic transit…
We study the q-dependent susceptibility chi(q) of a series of quasiperiodic Ising models on the square lattice. Several different kinds of aperiodic sequences of couplings are studied, including the Fibonacci and silver-mean sequences. Some identities and theorems are generalized and simpler derivations are presented. We find that the q-dependent susceptibilities are periodic, with the commensurate peaks of chi(q) located at the same positions as for the regular Ising models. Hence, incommensurate everywhere-dense peaks can only occur in cases with mixed ferromagnetic-antiferromagnetic interac…
The static and dynamic critical properties of the ferromagnetic q-state Potts models on a square lattice with q = 2 and 3 are numerically studied via the nonequilibrium relaxation method. The relaxation behavior of both the order parameter and energy as well as that of the second moments are investigated, from which static and dynamic critical exponents can be obtained. We find that the static exponents thus obtained from the relaxation of the order parameter and energy together with the second moments of the order parameter exhibit a close agreement with the exact exponents, especially for th…
We study random dense packings of Heisenberg dipoles by numerical simulation. The dipoles are at the centers of identical spheres that occupy fixed random positions in space and fill a fraction $Φ$ of the spatial volume. The parameter $Φ$ ranges from rather low values, typical of amorphous ensembles, to the maximum $Φ$=0.64 that occurs in the random-close-packed limit. We assume that the dipoles can freely rotate and have no local anisotropies. As well as the usual thermodynamical variables, the physics of such systems depends on $Φ$. Concretely, we explore the magnetic ordering of these syste…
Self-organization to ferromagnetic phase transition in cellular automata of spins governed by stochastic majority rule and when topology between spins is changed, is investigated numerically. Three types of edge rewiring are considered. The algorithm of Watts and Strogatz is applied at each time step to establish a network evolving stochastically (the first network). The preference functions are defined to amplify the role of strongly connected vertices (the second network). Demand to preserve graph connectivity provides the third way of edge rewiring. Each of these processes yields the differ…
We study the model of a biaxial single ferromagnetic spin Hamiltonian with an external magnetic field applied along the medium axis. The phase transition of the escape rate is investigated. Two different but equivalent methods are implemented. Firstly, we derive the semi-classical description of the model which yields a potential and a coordinate dependent mass. Secondly, we employ the method of spin-particle mapping which yields a similar potential to that of semi-classical description but with a constant mass. The exact instanton trajectory and its corresponding action, which have not been r…
Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely connected structure, have become well understood. Many features generalize to sparse Erdos-Renyi graph structures above the percolation threshold, and to Bethe lattices when appropriate boundary conditions apply. In this paper we consider spin states subject to a combination of sparse strong interactions with weak dense interactions, which we term a composite model.…
We study the phase diagram of the ferromagnetic $q$-state Potts model on the various three-dimensional lattices for integer and non-integer values of $q>1$. Our approach is based on a thermodynamically self-consistent Ornstein-Zernike approximation for the two-point correlation functions. We calculate the transition temperatures and, when the transition is first order, the jump discontinuities in the magnetization and the internal energy, as well as the coordinates of the critical endpoint in external field. Our predictions are in very good agreement with best available estimates. From the num…
Two predictions are made for properties of the ferromagnetic superconductors discovered recently. The first one is that spin-triplet, p-wave pairing in such materials will give the magnons a mass inversely proportional to the square of the magnetization. The second one is based on a specific mechanism for p-wave pairing, and predicts that the observed broad anomaly in the specific heat of URhGe will be resolved into a split transition with increasing sample quality. These predictions will help discriminate between different possible mechanisms for ferromagnetic superconductivity.
By means of extensive computer simulations we analyze in detail the two dimensional $\pm J$ Ising spin glass with ferromagnetic next-nearest-neighbor interactions. We found a crossover from ferromagnetic to ``spin glass'' like order both from numerical simulations and analytical arguments. We also present evidences of a second crossover from the ``spin glass'' behavior to a paramagnetic phase for the largest volume studied.
As is known, at the Gibbs-Boltzmann equilibrium, the mean-field $q$-state Potts model with a ferromagnetic coupling has only a first order phase transition when $q\geq 3$, while there is no phase transition for an antiferromagnetic coupling. The same equilibrium is asymptotically reached when one considers the continuous time evolution according to a Glauber dynamics. In this paper we show that, when we consider instead the Potts model evolving according to a discrete-time dynamics, the Gibbs-Boltzmann equilibrium is reached only when the coupling is ferromagnetic while, when the coupling is a…
The transverse field in the quantum Ising chain is linearly ramped from the para- to the ferromagnetic phase across the quantum critical point at a rate characterized by a quench time $τ_Q$. We calculate a connected kink-kink correlator in the final state at zero transverse field. The correlator is a sum of two terms: a negative (anti-bunching) Gaussian that depends on the Kibble-Zurek (KZ) correlation length only and a positive term that depends on a second longer scale of length. The second length is made longer by dephasing of the state excited near the critical point during the following r…
Magnetic properties of the two-dimensional spin-polarized Fermi gas with dipole-dipole interaction are studied in the presence of external magnetic field at zero temperature. Within perturbation theory and the second quantization formalism, the total energy is explicitly obtained as a function of three dimensionless parameters, the spin polarization, dipolar coupling and Zeeman parameters. We examine the effects of these agents on the magnetic properties of 2D Fermi gas. The results show that an induced ferromagnetic phase transition is observed only for adequately large values of magnetic fie…
In this paper we analytically study the recurrence equations of an Ising model with three competing interactions on a Cayley tree of order three. We exactly describe paramagnetic and ferromagnetic phases of the Ising model. We obtain some rigorous results: critical temperatures and curves, number of phases, partition function. Ganikhodjaev et al. [J. Concrete and Applicable Mathematics, 9 (1), 26-34 (2011)] have numerically studied the Ising model on a second-order Cayley tree. We compare the numerical results to exact solutions of mentioned model.
The Monte Carlo analysis for the magnetic response of a single-walled nanotube using the Metropolis and Wang Landau algorithms is reported in the present paper. The nanotube architecture used in the present study utilizes the spin half Ising model with nearest neighbors interaction and obtained various magnetic orderings namely, ferromagnetic, G-type anti-ferromagnetic, A-type anti-ferromagnetic, and C-type anti-ferromagnetic. It is also found that the phase changes from ferromagnetic/anti-ferromagnetic to paramagnetic with the modification of system's control parameters. The transition temper…
We present Monte Carlo simulations of the spanning-forest model (q \to 0 limit of the ferromagnetic Potts model) in spatial dimensions d=3,4,5. We show that, in contrast to the two-dimensional case, the model has a "ferromagnetic" second-order phase transition at a finite positive value w_c. We present numerical estimates of w_c and of the thermal and magnetic critical exponents. We conjecture that the upper critical dimension is 6.
We study the $\pm J$ three-dimensional Ising model with a spatially uniaxially anisotropic bond randomness on the simple cubic lattice. The $\pm J$ random exchange is applied in the $xy$ planes, whereas in the z direction only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied, at the ferromagnetic-paramagnetic transition line, using parallel tempering and a convenient concentration of antiferromagnetic bonds ($p_z=0 ; p_{xy}=0.176$). The numerical data point out clearly to a second-order ferromagnet…
The second order para-ferromagnetic phase transition in a series of amorphous alloys (Fe{_5}Co{_{50}}Ni{_{17-x}}Cr{_x}B{_{16}}Si{_{12}}) is investigated using nonlinear susceptibility. A simple molecular field treatment for the critical region shows that the third order suceptibility (chi{_3}) diverges on both sides of the transition temperature, and changes sign at T{_C}. This critical behaviour is observed experimentally in this series of amorphous ferromagnets, and the related assymptotic critical exponents are calculated. It is shown that using the proper scaling equations, all the exponen…
It is generally believed that a dilute spin-1/2 Fermi gas with repulsive interactions can undergo a ferromagnetic phase transition to a spin-polarized state at a critical gas parameter $(k_{\rm F}a)_c$. Previous theoretical predictions of the ferromagnetic phase transition have been based on the perturbation theory, which treats the gas parameter as a small number. On the other hand, Belitz, Kirkpatrick, and Vojta (BKV) have argued that the phase transition in clean itinerant ferromagnets is generically of first order at low temperatures, due to the correlation effects that lead to a nonanalyt…
