Searcharxiv⌕ Search

arXiv subjects

Ferenc Igloi

Publications and source records attributed to Ferenc Igloi.

41 records · Page 3Linked to original sources
arXiv1996

Surface Magnetisation and Surface Correlations in Aperiodic Ising Models

We consider the surface critical behaviour of diagonally layered Ising models on the square lattice where the inter-layer couplings follow some aperiodic sequence. The surface magnetisation is analytically evaluated from a simple formula derived by the diagonal transfer matrix method, while the surface spin-spin correlations are obtained numerically by a recursion method, based on the star-triangle transformation. The surface critical behaviour of different aperiodic Ising models are found in accordance with the corresponding relevance-irrelevance criterion. For marginal sequences the critical exponents are continuously varying with the strength of aperiodicity and generally the systems follow anisotropic scaling at the critical point.

cond-mat↗
arXiv1996

Interface Fluctuations on a Hierarchical Lattice

We consider interface fluctuations on a two-dimensional layered lattice where the couplings follow a hierarchical sequence. This problem is equivalent to the diffusion process of a quantum particle in the presence of a one-dimensional hierarchical potential. According to a modified Harris criterion this type of perturbation is relevant and one expects anomalous fluctuating behavior. By transfer-matrix techniques and by an exact renormalization group transformation we have obtained analytical results for the interface fluctuation exponents, which are discontinuous at the homogeneous lattice limit.

cond-mat↗
arXiv1995

Critical Behavior of Hierarchical Ising Models

We consider the critical behavior of two-dimensional layered Ising models where the exchange couplings between neighboring layers follow hierarchical sequences. The perturbation caused by the non-periodicity could be irrelevant, relevant or marginal. For marginal sequences we have performed a detailed study, which involved analytical and numerical calculations of different surface and bulk critical quantities in the two-dimensional classical as well as in the one-dimensional quantum version of the model. The critical exponents are found to vary continuously with the strength of the modulation, while close to the critical point the system is essentially anisotropic: the correlation length is diverging with different exponents along and perpendicular to the layers.

cond-mat↗
arXiv1994

Correlations in Random Ising Chains at Zero Temperature

We present a general method to calculate the connected correlation function of random Ising chains at zero temperature. This quantity is shown to relate to the surviving probability of some one-dimensional, adsorbing random walker on a finite intervall, the size of which is controlled by the strength of the randomness. For different random field and random bond distributions the correlation length is exactly calculated.

cond-mat↗