Related papers: 3D Ising Model:The Scaling Equation of State
We study the behaviour of a universal combination of susceptibility and correlation length in the Ising model in two and three dimensions, in presence of both magnetic and thermal perturbations, in the neighbourhood of the critical point.…
We show analytically that the perturbative expansion for the free energy of the zero dimensional (quenched) disordered Ising model is Borel-summable in a certain range of parameters, provided that the summation is carried out in two steps:…
Renormalization group, and in particular its Quantum Field Theory implementation has provided us with essential tools for the description of the phase transitions and critical phenomena beyond mean field theory. We therefore review the…
We calculate the dynamic critical exponent $z$ for 2d and 3d Ising universality classes by means of minimally subtracted five-loop $\varepsilon$ expansion obtained for the one-component model A. This breakthrough turns out to be possible…
We investigate the critical behavior of three-dimensional random-field Ising systems with both Gauss and bimodal distribution of random fields and additional the three-dimensional diluted Ising antiferromagnet in an external field. These…
We consider the mass spectrum of the 3$d$ 3-state Potts model in the broken phase (a) near the second order Ising critical point in the temperature - magnetic field plane and (b) near the weakly first order transition point at zero magnetic…
The bulk and boundary magnetizations are calculated for the critical Ising model on a randomly triangulated disk in the presence of a boundary magnetic field h. In the continuum limit this model corresponds to a c = 1/2 conformal field…
The BEST Collaboration equation of state combining lattice data with the 3D Ising critical point encounters limitations due to the truncated Taylor expansion up to $\frac{\mu_B}{T} \sim 2.5$. This truncation consequently restricts its…
We study the probability distribution P(M) of the order parameter (average magnetization) M, for the finite-size systems at the critical point. The systems under consideration are the 3-dimensional Ising model on a simple cubic lattice, and…
The n-vicinities method for approximate calculations of the partition function of a spin system was proposed previously. The equation of state was obtained in the most general form. In the present publication these results are adapted to…
In the presented article we present an algorithm for the computation of ground state spin configurations for the 2d random bond Ising model on planar triangular lattice graphs. Therefore, it is explained how the respective ground state…
A lot of progress has been made recently in our understanding of the random-field Ising model thanks to large-scale numerical simulations. In particular, it has been shown that, contrary to previous statements: the critical exponents for…
Critical finite-size scaling functions for the order parameter distribution of the two and three dimensional Ising model are investigated. Within a recently introduced classification theory of phase transitions, the universal part of the…
The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation…
We discuss first order transitions for systems in the Ising universality class. The critical long distance physics near the endpoint of the critical line is explicitly connected to microscopic properties of a given system. Information about…
The ground state energy and entropy of the dilute mean field Ising model is computed exactly by a single order parameter. An analogous exact solution is obtained in presence of a magnetic field with random locations. Results allow for a…
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…
It is often assumed that for treating numerical (or experimental) data on continuous transitions the formal analysis derived from the Renormalization Group Theory can only be applied over a narrow temperature range, the "critical region";…
Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of Statistical Physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In…
The detailed analysis of the global structure of the renormalization-group (RG) flow diagram for a model with isotropic and cubic interactions is carried out in the framework of the massive field theory directly in three dimensions (3D)…