Dynamical phase transition in one-dimensional kinetic Ising model with nonuniform coupling constants

An extension of the Kinetic Ising model with nonuniform coupling constants on a one-dimensional lattice with boundaries is investigated, and the relaxation of such a system towards its equilibrium is studied. Using a transfer matrix method, it is shown that there are cases where the system exhibits a dynamical phase transition. There may be two phases, the fast phase and the slow phase. For some region of the parameter space, the relaxation time is independent of the reaction rates at the boundaries. Changing continuously the reaction rates at the boundaries, however, there is a point where the relaxation times begins changing, as a continuous (nonconstant) function of the reaction rates at the boundaries, so that at this point there is a jump in the derivative of the relaxation time with respect to the reaction rates at the boundaries.Comment: 17 page

Ground state numerical study of the three-dimensional random field Ising model

The random field Ising model in three dimensions with Gaussian random fields is studied at zero temperature for system sizes up to 60^3. For each realization of the normalized random fields, the strength of the random field, Delta and a uniform external, H is adjusted to find the finite-size critical point. The finite-size critical point is identified as the point in the H-Delta plane where three degenerate ground states have the largest discontinuities in the magnetization. The discontinuities in the magnetization and bond energy between these ground states are used to calculate the magnetization and specific heat critical exponents and both exponents are found to be near zero.Comment: 10 pages, 6 figures; new references and small changes to tex

On the nature of the phase transition in the three-dimensional random field Ising model

A brief survey of the theoretical, numerical and experimental studies of the random field Ising model during last three decades is given. Nature of the phase transition in the three-dimensional RFIM with Gaussian random fields is discussed. Using simple scaling arguments it is shown that if the strength of the random fields is not too small (bigger than a certain threshold value) the finite temperature phase transition in this system is equivalent to the low-temperature order-disorder transition which takes place at variations of the strength of the random fields. Detailed study of the zero-temperature phase transition in terms of simple probabilistic arguments and modified mean-field approach (which take into account nearest-neighbors spin-spin correlations) is given. It is shown that if all thermally activated processes are suppressed the ferromagnetic order parameter m(h) as the function of the strength $h$ of the random fields becomes history dependent. In particular, the behavior of the magnetization curves m(h) for increasing and for decreasing $h$ reveals the hysteresis loop.Comment: 22 pages, 12 figure

Percolation in three-dimensional random field Ising magnets

The structure of the three-dimensional random field Ising magnet is studied by ground state calculations. We investigate the percolation of the minority spin orientation in the paramagnetic phase above the bulk phase transition, located at [Delta/J]_c ~= 2.27, where Delta is the standard deviation of the Gaussian random fields (J=1). With an external field H there is a disorder strength dependent critical field +/- H_c(Delta) for the down (or up) spin spanning. The percolation transition is in the standard percolation universality class. H_c ~ (Delta - Delta_p)^{delta}, where Delta_p = 2.43 +/- 0.01 and delta = 1.31 +/- 0.03, implying a critical line for Delta_c < Delta <= Delta_p. When, with zero external field, Delta is decreased from a large value there is a transition from the simultaneous up and down spin spanning, with probability Pi_{uparrow downarrow} = 1.00 to Pi_{uparrow downarrow} = 0. This is located at Delta = 2.32 +/- 0.01, i.e., above Delta_c. The spanning cluster has the fractal dimension of standard percolation D_f = 2.53 at H = H_c(Delta). We provide evidence that this is asymptotically true even at H=0 for Delta_c < Delta <= Delta_p beyond a crossover scale that diverges as Delta_c is approached from above. Percolation implies extra finite size effects in the ground states of the 3D RFIM.Comment: replaced with version to appear in Physical Review

Disorder, Order, and Domain Wall Roughening in the 2d Random Field Ising Model

Ground states and domain walls are investigated with exact combinatorial optimization in two-dimensional random field Ising magnets. The ground states break into domains above a length scale that depends exponentially on the random field strength squared. For weak disorder, this paramagnetic structure has remnant long-range order of the percolation type. The domain walls are super-rough in ordered systems with a roughness exponent $\zeta$ close to 6/5. The interfaces exhibit rare fluctuations and multiscaling reminiscent of some models of kinetic roughening and hydrodynamic turbulence.Comment: to be published in Phys.Rev.E/Rapid.Com

Effects of Pore Walls and Randomness on Phase Transitions in Porous Media

We study spin models within the mean field approximation to elucidate the topology of the phase diagrams of systems modeling the liquid-vapor transition and the separation of He$^3$--He$^4$ mixtures in periodic porous media. These topologies are found to be identical to those of the corresponding random field and random anisotropy spin systems with a bimodal distribution of the randomness. Our results suggest that the presence of walls (periodic or otherwise) are a key factor determining the nature of the phase diagram in porous media.Comment: REVTeX, 11 eps figures, to appear in Phys. Rev.