相关论文: Finite size scaling in Ising-like systems with que…

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…

In the context of Monte Carlo simulations, the analysis of the probability distribution $P_L(m)$ of the order parameter $m$, as obtained in simulation boxes of finite linear extension $L$, allows for an easy estimation of the location of…

The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size…

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…

In addition to the standard scaling rules relating critical exponents at second order transitions, hyperscaling rules involve the dimension of the model. It is well known that in canonical Ising models hyperscaling rules are modified above…

We present a unified view of finite-size scaling (FSS) in dimension d above the upper critical dimension, for both free and periodic boundary conditions. We find that the modified FSS proposed some time ago to allow for violation of…

We study the critical behavior of the Ising model in annealed scale-free (SF) networks of finite system size with forced upper cutoff in degree. By mapping the model onto the weighted fully connected Ising model, we derive analytic results…

We present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behavior of these systems is affected by slowly-decaying scaling…

We use computer simulations to investigate the extended phase diagram of a supercooled liquid linearly coupled to a quenched reference configuration. An extensive finite-size scaling analysis demonstrates the existence of a random-field…

We show numerically that correlation length at the critical point in the five-dimensional Ising model varies with system size L as L^{5/4}, rather than proportional to L as in standard finite size scaling (FSS) theory. Our results confirm a…

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…

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…

We rederive the finite size scaling formula for the apparent critical temperature by using Mean Field Theory for the Ising Model above the upper critical dimension. We have also performed numerical simulations in five dimensions and our…

The critical behavior of a quenched random hypercubic sample of linear size $L$ is considered, within the ``random-$T_{c}$'' field-theoretical mode, by using the renormalization group method. A finite-size scaling behavior is established…

We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…

The influence of a thermodynamic constraint on the critical finite-size scaling behavior of three-dimensional Ising and XY models is analyzed by Monte-Carlo simulations. Within the Ising universality class constraints lead to Fisher…

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…

Analytic phenomenological scaling is carried out for the random field Ising model in general dimensions using a bar geometry. Domain wall configurations and their decorated profiles and associated wandering and other exponents…

The hyperscaling relation and standard finite-size scaling (FSS) are known to break down above the upper critical dimension due to dangerous irrelevant variables. We establish a coherent formalism for FSS at quantum phase transitions above…

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…