Related papers: On Finite Size Effects in $d=2$ Quantum Gravity
Finite-size scaling at fixed renormalization-group invariant is a powerful and flexible technique to analyze Monte Carlo data at a critical point. It consists in fixing a given renormalization-group invariant quantity to a given value,…
The correlation function of the two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor expansion are…
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 formulate a quantum formalism for the statistical mechanical models of discretized field theories on lattices and then show that the discrete version of $\phi^4$ theory on 2D square lattice is complete in the sense that the partition…
In lattice quantum field theories with topological sectors, simulations at fine lattice spacings --- with typical algorithms --- tend to freeze topologically. In such cases, specific topological finite size effects have to be taken into…
The finite-size scaling properties of the quantum Ising chain with different types of generalized defects are studied. These not only mean an alteration of the coupling constant as previously examined, but an additional arbitrary…
Accurate Monte Carlo data from a set of isotherms near the critical point are analyzed using two RG based complementary representations, given respectively in terms of $\bar h=h/\mid t \mid^{\beta\delta}$ and $\bar…
Using the mapping of the partition function of the two-dimensional Ising model onto a pfaffian we evaluate the domain wall free energy difference for the pure and disordered Ising model close to the pure fixed point. Using this method very…
Form factor representation of the correlation function of the 2D Ising model on a cylinder is generalized to the case of arbitrary disposition of correlating spins. The magnetic susceptibility on a lattice, one of whose dimensions ($N$) is…
We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings,…
Quantum gravity is investigated in the limit of a large number of space-time dimensions, using as an ultraviolet regularization the simplicial lattice path integral formulation. In the weak field limit the appropriate expansion parameter is…
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…
We study the scaling properties of the statistics of the work done on a generic many-body system at a quantum phase transition of any order and type, arising from quenches of a driving control parameter. For this purpose we exploit a…
Finite-size and surface effects in fine particle systems are investigated by Monte Carlo simulation of a model of a $\gamma$-Fe$_2$O$_3$ (maghemite) single particle. Periodic boundary conditions have been used to simulate the bulk…
The influence of periodic boundary conditions (implicit finite-size effects) on the anisotropy of pair correlations in computer simulations is studied for a dense classical fluid of pair-wise interacting krypton atoms near the triple point.…
In the two-dimensional Ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point. We study this question by extensive Monte Carlo simulations for various strength of disorder. The…
The soft breaking of gauge or other symmetries is the typical Quantum Field Theory phenomenon. In many cases one can apply the St$\ddot{\rm u}$ckelberg procedure, which means introducing some additional field or fields and restore the gauge…
Gravity is perturbatively renormalizable for the physical states which can be conveniently defined via foliation-based quantization. In recent sequels, one-loop analysis was explicitly carried out for Einstein-scalar and Einstein-Maxwell…
Ever since the first discovery of Poynting and Robertson, the radiation source has been treated as merely a point. Even in a very few studies where the size of the source has been taken into account, the treatment of the problem remained…
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…