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 numerical data are in a good agreement with the Mean Field theoretical predictions, in particular, with the finite size exponent of the connected susceptibility...

Metabolic rate, heart rate, lifespan, and many other physiological properties vary with body mass in systematic and interrelated ways. Present empirical data suggest that these scaling relationships take the form of power laws with exponents that are simple multiples of one quarter. A compelling explanation of this observation was put forward a decade ago by West, Brown, and Enquist (WBE). Thei...

abstract. in this paper we study some relations between the power andquotient power graph of a finite group. these interesting relations motivateus to find some graph theoretical properties of the quotient power graphand the proper quotient power graph of a finite group g. in addition, weclassify those groups whose quotient (proper quotient) power graphs areisomorphic to trees or paths.

The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling t...

To explore the character of the underlying transport in plasma turbulence, we have followed the motion of pseudo-particle tracers during the nonlinear evolution of three-dimensional turbulence models. These calculations have been performed for three different turbulence models and are associated with resistive interchange, resistive ballooning, and ηi modes, respectively. The finite-scale Lyapu...

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 the Fisher zeroes of the model. Moreover, exact results are also determined for the scaling of the specific heat at criticality, for the specific-heat peak ...

Let G be an abelian group of bounded exponent and A ⊂ G. We show that if the collection of translates of A has VC dimension at most d, then for every > 0 there is a subgroup H of G of index at most −d−o(1) such that one can add or delete at most |G| elements to A to make it a union of H-cosets. We also establish a removal lemma with polynomial bounds, with applications to property testing, for ...

We study the possible link between “local turbulence strength” in a flow which is represented by a finite time series and a “chaotic invariant”, namely, the leading Lyaponuv exponent that characterizes this series. To validate a conjecture about this link, we analyze several time series of measurements taken by a plane flying at constant height in the upper troposphere. For each of these time s...

At finite temperature we study the quantum tunneling of magnetization for a small ferromagnetic particle with the biaxial symmetry placed in a magnetic field at an arbitrary angle. We present numerical WKB exponent below the crossover temperature in which the quantum tunneling is affected by the thermal activation, and the approximate form of the WKB exponent around the crossover region. The ef...

We study the synchronization transition in scale-free networks that display power-law asymptotic behaviors in their degree distributions. The critical coupling strength and the order-parameter critical exponent derived by the mean-field approach depend on the degree exponent lambda, which implies a close connection between structural organization and the emergence of dynamical order in complex ...