Related papers: Scaling above the upper critical dimension in Isin…
We investigate a two-dimensional Ising model with long-range interactions that emerge from a generalization of the magnetic dipolar interaction in spin systems with in-plane spin orientation. This interaction is, in general, anisotropic…
We progress finite-size scaling in systems with free boundary conditions above their upper critical dimension, where in the thermodynamic limit critical scaling is described by mean-field theory. Recent works show that the correlation…
Universality classes encompass the analogous thermodynamic behavior of unlike physical systems, at different spatial dimensions $d$, in the vicinity of their critical point. Critical exponents define these classes, with the Ising model…
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…
Among the Renormalization Group Theory scaling rules relating critical exponents, there are hyperscaling rules involving the dimension of the system. It is well known that in Ising models hyperscaling breaks down above the upper critical…
The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension $d=2$ to 7 with periodic boundary conditions. The critical exponents associated to the Finite-Size Scaling of the magnetic susceptibility are…
The disorder-driven phase transition of the RFIM is observed using exact ground-state computer simulations for hyper cubic lattices in d=5,6,7 dimensions. Finite-size scaling analyses are used to calculate the critical point and the…
In three dimensions, or more generally, below the upper critical dimension, scaling laws for critical phenomena seem well understood, for both infinite and for finite systems. Above the upper critical dimension of four, finite-size scaling…
We introduce a universal combination of susceptibility and correlation length in the 3D Ising model, depending both on temperature and external magnetic field. Starting from a parametric representation of the equation of state, we study its…
Although the fully connected Ising model does not have a length scale, we show that its critical exponents can be found using finite size scaling with the scaling variable equal to N, the number of spins. We find that at the critical…
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.…
It was recently shown [Phys. Rev. Lett. {\bf 110}, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming…
The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz is analysed. Leading and sub-dominant scaling behaviour of the Fisher zeroes are determined exactly. The finite-size scaling, with corrections, of…
In this paper we apply the formalism of translation invariant (continuous) matrix product states in the thermodynamic limit to $(1+1)$ dimensional critical models. Finite bond dimension bounds the entanglement entropy and introduces an…
There has been a long running debate on the finite size scaling for the Ising model with free boundary conditions above the upper critical dimension, where the standard picture gives a $L^2$ scaling for the susceptibility and an alternative…
We study numerically the region above the critical temperature of the four dimensional Random Field Ising Model. Using a cluster dynamic we measure the connected and disconnected magnetic susceptibility and the connected and disconnected…
In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a…
Validity of modified finite-size scaling above the upper critical dimension is demonstrated for the quantum phase transition whose dynamical critical exponent is $z=2$. We consider the $N$-component Bose-Hubbard model, which is exactly…
Above the upper critical dimension, the breakdown of hyperscaling is associated with dangerous irrelevant variables in the renormalization group formalism at least for systems with periodic boundary conditions. While these have been…
The two-dimensional Ising model with Brascamp-Kunz boundary conditions has a partition function more amenable to analysis than its counterpart on a torus. This fact is exploited to exactly determine the full finite-size scaling behaviour of…