arXiv subjects

Gábor Palágyi

Publications and source records attributed to Gábor Palágyi.

3 recordsLinked to original sources

arXiv1999

Boundary critical behaviour of two-dimensional random Potts models

We consider random q-state Potts models for $3\le q \le 8$ on the square lattice where the ferromagnetic couplings take two values $J_1>J_2$ with equal probabilities. For any q the model exhibits a continuous phase transition both in the bulk and at the boundary. Using Monte Carlo techniques the surface and the bulk magnetizations are studied close to the critical temperature and the critical exponents $β_1$ and $β$ are determined. In the strip-like geometry the critical magnetization profile is investigated with free-fixed spin boundary condition and the characteristic scaling dimension, $β_1/ν$, is calculated from conformal field theory. The critical exponents and scaling dimensions are found monotonously increasing with q. Anomalous dimensions of the relevant scaling fields are estimated and the multifractal behaviour at criticality is also analyzed.

cond-mat.stat-mech↗

arXiv1998

The McCoy-Wu Model in the Mean-field Approximation

We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu model) and study its critical properties in the frame of mean-field theory. In the low-temperature phase there is an average spontaneous magnetization in the system, which vanishes as a power law at the critical point with the critical exponents $β\approx 3.6$ and $β_1 \approx 4.1$ in the bulk and at the surface of the system, respectively. The singularity of the specific heat is characterized by an exponent $α\approx -3.1$. The samples reduced critical temperature $t_c=T_c^{av}-T_c$ has a power law distribution $P(t_c) \sim t_c^ω$ and we show that the difference between the values of the critical exponents in the pure and in the random system is just $ω\approx 3.1$. Above the critical temperature the thermodynamic quantities behave analytically, thus the system does not exhibit Griffiths singularities.

cond-mat.stat-mech↗

arXiv1994

Local critical behaviour at aperiodic surface extended perturbation in the Ising quantum chain

The surface critical behaviour of the semi--infinite one--dimensional quantum Ising model in a transverse field is studied in the presence of an aperiodic surface extended modulation. The perturbed couplings are distributed according to a generalized Fredholm sequence, leading to a marginal perturbation and varying surface exponents. The surface magnetic exponents are calculated exactly whereas the expression of the surface energy density exponent is conjectured from a finite--size scaling study. The system displays surface order at the bulk critical point, above a critical value of the modulation amplitude. It may be considered as a discrete realization of the Hilhorst--van Leeuwen model.

cond-mat↗