Search results for "Ising Model"
showing 10 items of 241 documents
On the merit of a Central Limit Theorem-based approximation in statistical physics
2012
The applicability conditions of a recently reported Central Limit Theorem-based approximation method in statistical physics are investigated and rigorously determined. The failure of this method at low and intermediate temperature is proved as well as its inadequacy to disclose quantum criticalities at fixed temperatures. Its high temperature predictions are in addition shown to coincide with those stemming from straightforward appropriate expansions up to (k_B T)^(-2). Our results are clearly illustrated by comparing the exact and approximate temperature dependence of the free energy of some exemplary physical systems.
Entanglement continuous unitary transformations
2016
Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a diagonal or block-diagonal form in second quantization. Yet, one of their main challenges is how to approximate the infinitely-many coupled differential equations that are produced throughout this flow. Here we show that tensor networks offer a natural and non-perturbative truncation scheme in terms of entanglement. The corresponding scheme is called "entanglement-CUT" or eCUT. It can be used to extract the low-energy physics of quantum many-body Hamiltonians, including quasiparticle energy gaps. We…
Spherical random-field systems with long-range interactions: general results and application to the Coulomb glass
1993
A classical spherical random-field Hamiltonian with long-range (power-law) interactions is investigated by means of the replica theory. Both ferromagnetic and anti-ferromagnetic interactions are considered. The use of continuous variables instead of Ising variables in the spherical version of the model allows one to calculate the free energy exactly. The existence of an equilibrium phase transition is investigated based on the replica-symmetric solution. The results are applied to the Coulomb-glass model of interacting localized electrons in a disordered solid. This model is shown not to have an equilibrium phase transition for spatial dimensions D 4 the model has a phase transition to an o…
Linear response in multipolar glasses
1988
We consider the unified hamiltonian with a bilinear coupling, describing the Ising-, vector-, Potts-, octupolar-glass and other glasses [1, 2]. We systematically derive the response to a homogeneous tensor-field as well as the response to an inhomogeneous random tensor-field. We investigate the overlap distribution function and its first and second moment. In all these considerations, we recover the results of the Ising spin glass for sufficiently symmetric multipolar glasses, but we also obtain differnt results for less symmetric glasses.
Spin-one-Ising model for (CO)1?x (N2) x mixtures: A finite size scaling study of random-field-type critical phenomena
1995
A qualitative model for solid mixtures of diatomic molecules, where one species (called CO, to be specific) carries both a dipole moment and a quadrupole moment, while the other species (calledN 2) has only a quadrupole moment, is studied by Monte Carlo methods. We use spinsS i =±1 to represent the orientations of the CO electric dipole moment, if the lattice sitei is taken by a CO molecule, whileS i =0 if the site is taken by anN 2 molecule. Assuming nearest-neighbor antiferroelectric interactions between CO molecules, and a bilinear dipole-quadrupole coupling between CO andN 2, the randomly quenchedN 2 molecules act like random fields do in the random field Ising model. In previous work i…
Kinetic-Ising-model description of Newtonian dynamics: A one-dimensional example.
1993
We show that the Newtonian dynamics of a chain of particles with an anharmonic on-site potential and harmonic nearest-neighbor interactions can be described by a one-dimensional kinetic Ising model with most general Glauber transition rates, provided the temperature is low enough compared to the minimum barrier height. The transition rates are calculated by use of the transition-state theory. At higher temperatures, memory effects occur which invalidate this kinetic description. These memory effects are due to the appearance of dynamically correlated clusters of particles performing periodic oscillations over a certain time scale.
Fluctuations and lack of self-averaging in the kinetics of domain growth
1986
The fluctuations occurring when an initially disordered system is quenched at timet=0 to a state, where in equilibrium it is ordered, are studied with a scaling theory. Both the mean-sizel(t)d of thed-dimensional ordered domains and their fluctuations in size are found to increase with the same power of the time; their relative size fluctuations are independent of the total volumeLd of the system. This lack of self-averaging is tested for both the Ising model and the φ4 model on the square lattice. Both models exhibit the same lawl(t)=(Rt)x withx=1/2, although the φ4 model has “soft walls”. However, spurious results withx≷1/2 are obtained if “bad” pseudorandom numbers are used, and if the n…
Scaling Regimes and the Singularity of Specific Heat in the 3D Ising Model
2013
AbstractThe singularity of specific heat CV of the three-dimensional Ising model is studied based on Monte Carlo data for lattice sizes L≤1536. Fits of two data sets, one corresponding to certain value of the Binder cumulant and the other — to the maximum of CV, provide consistent values of C0 in the ansatz CV(L)=C0+ALα/ν at large L, if α/ν=0.196(6). However, a direct estimation from our data suggests that α/ν, most probably, has a smaller value (e.g., α/ν= 0.113(30)). Thus, the conventional power-law scaling ansatz can be questioned because of this inconsistency. We have found that the data are well described by certain logarithmic ansatz.
One-dimensional Ising-like systems: an analytical investigation of the static and dynamic properties, applied to spin-crossover relaxation
2000
We investigate the dynamical properties of the 1-D Ising-like Hamiltonian taking into account short and long range interactions, in order to predict the static and dynamic behavior of spin crossover systems. The stochastic treatment is carried out within the frame of the local equilibrium method [1]. The calculations yield, at thermodynamic equilibrium, the exact analytic expression previously obtained by the transfer matrix technique [2]. We mainly discuss the shape of the relaxation curves: (i) for large (positive) values of the short range interaction parameter, a saturation of the relaxation curves is observed, reminiscent of the behavior of the width of the static hysteresis loop [3]; …
Ising Spin-Glass on a Lattice with Small Loops
1991
We consider the Ising spin-glass on a special lattice containing small loops with finite coordination number c. We derive the equation for the effective field distribution. With zero external field, we calculate the spin-glass transition temperature and obtain the lower critical dimension of the system. We investigate the system near and below the spin-glass transition and find that the replica symmetric solution is unstable in the low-temperature phase. Our results indicate that the replica symmetry breaking (RSB) effects are stronger than that of the Bethe lattice and furthermore, RSB is enhanced as the dimension (c/2) is decreased. Comparison with recent results of the 1/d expansion is a…