Critical exponents for Ising-like systems on Sierpinski carpets
نویسندگان
چکیده
2014 The critical properties of Ising models on various fractal lattices of the Sierpinski carpet type are studied using numerical simulations. We observe scaling and measure the exponents 03B3 and 03BD which are then compared to the values which have been recently extrapolated from the Wilson-Fisher 03B5-expansion in non integer dimensions. It appears that in the general case an effective dimension, in addition to the Hausdorf dimension, is needed to describe the critical behaviour. When these dimensions are equal, our results are then compatible with the conjecture that the fractal lattice could interpolate regular lattices in non integer dimensions. J. Physique 48 (1987) 553-558 AVRIL 1987, Classification Physics Abstracts 05.05 75.10H
منابع مشابه
Critical properties of Ising model on Sierpinski fractals . A finite size scaling analysis approach
The present paper focuses on the order-disorder transition of an Ising model on a self-similar lattice. We present a detailed numerical study, based on the Monte Carlo method in conjunction with the finite size scaling method, of the critical properties of the Ising model on some two dimensional deterministic fractal lattices with different Hausdorff dimensions. Those with finite ramification o...
متن کاملChange in order of phase transitions on fractal lattices
We reexamine a population model which exhibits a continuous absorbing phase transition belonging to directed percolation in 1D and a first-order transition in 2D and above. Studying the model on Sierpinski Carpets of varying fractal dimensions, we examine at what fractal dimension 1 ≤ d f ≤ 2, the change in order occurs. As well as commenting on the order of the transitions, we produce estimate...
متن کاملHigh order perturbation study of the frustrated quantum Ising chain
In this paper, using high order perturbative series expansion method, the critical exponents of the order parameter and susceptibility in transition from ferromagnetic to disordered phases for 1D quantum Ising model in transverse field, with ferromagnetic nearest neighbor and anti-ferromagnetic next to nearest neighbor interactions, are calculated. It is found that for small value of the frustr...
متن کاملDomain Growth on Percolation Structures
We discuss the dynamics of phase transformations following a quench from a high temperature disordered state to a state below the critical temperature in the case in which the system is not translationally invariant. In particular we consider the ordering dynamics on deterministic fractal substrates and on percolation networks by means of two models and both for non conserved order parameter an...
متن کاملCritical Behavior of the Ferromagnetic Ising Model on a Sierpiński Carpet: Monte Carlo Renormalization Group Study
We perform a Monte Carlo Renormalization Group analysis of the critical behavior of the ferromagnetic Ising model on a Sierpiński fractal with Hausdorff dimension df ≃ 1.8928. This method is shown to be relevant to the calculation of the critical temperature Tc and the magnetic eigen-exponent yh on such structures. On the other hand, scaling corrections hinder the calculation of the temperature...
متن کامل