Random Field and Random Anisotropy Effects in Defect-Free Three-Dimensional XY Models

Monte Carlo simulations have been used to study a vortex-free XY ferromagnet with a random field or a random anisotropy on simple cubic lattices. In the random field case, which can be related to a charge-density wave pinned by random point defects, it is found that long-range order is destroyed even for weak randomness. In the random anisotropy case, which can be related to a randomly pinned spin-density wave, the long-range order is not destroyed and the correlation length is finite. In both cases there are many local minima of the free energy separated by high entropy barriers. Our results for the random field case are consistent with the existence of a Bragg glass phase of the type discussed by Emig, Bogner and Nattermann.Comment: 10 pages, including 2 figures, extensively revise

Power-law correlations and orientational glass in random-field Heisenberg models

Monte Carlo simulations have been used to study a discretized Heisenberg ferromagnet (FM) in a random field on simple cubic lattices. The spin variable on each site is chosen from the twelve [110] directions. The random field has infinite strength and a random direction on a fraction x of the sites of the lattice, and is zero on the remaining sites. For x = 0 there are two phase transitions. At low temperatures there is a [110] FM phase, and at intermediate temperature there is a [111] FM phase. For x > 0 there is an intermediate phase between the paramagnet and the ferromagnet, which is characterized by a |k|^(-3) decay of two-spin correlations, but no true FM order. The [111] FM phase becomes unstable at a small value of x. At x = 1/8 the [110] FM phase has disappeared, but the power-law correlated phase survives.Comment: 8 pages, 12 Postscript figure

Topological Defects in the Random-Field XY Model and the Pinned Vortex Lattice to Vortex Glass Transition in Type-II Superconductors

As a simplified model of randomly pinned vortex lattices or charge-density waves, we study the random-field XY model on square ($d=2$) and simple cubic ($d=3$) lattices. We verify in Monte Carlo simulations, that the average spacing between topological defects (vortices) diverges more strongly than the Imry-Ma pinning length as the random field strength, $H$, is reduced. We suggest that for $d=3$ the simulation data are consistent with a topological phase transition at a nonzero critical field, $H_c$, to a pinned phase that is defect-free at large length-scales. We also discuss the connection between the possible existence of this phase transition in the random-field XY model and the magnetic field driven transition from pinned vortex lattice to vortex glass in weakly disordered type-II superconductors.Comment: LATEX file; 5 Postscript figures are available from [email protected]

Random Field Models for Relaxor Ferroelectric Behavior

Heat bath Monte Carlo simulations have been used to study a four-state clock model with a type of random field on simple cubic lattices. The model has the standard nonrandom two-spin exchange term with coupling energy $J$ and a random field which consists of adding an energy $D$ to one of the four spin states, chosen randomly at each site. This Ashkin-Teller-like model does not separate; the two random-field Ising model components are coupled. When $D / J = 3$, the ground states of the model remain fully aligned. When $D / J \ge 4$, a different type of ground state is found, in which the occupation of two of the four spin states is close to 50%, and the other two are nearly absent. This means that one of the Ising components is almost completely ordered, while the other one has only short-range correlations. A large peak in the structure factor $S (k)$ appears at small $k$ for temperatures well above the transition to long-range order, and the appearance of this peak is associated with slow, "glassy" dynamics. The phase transition into the state where one Ising component is long-range ordered appears to be first order, but the latent heat is very small.Comment: 7 pages + 12 eps figures, to appear in Phys Rev

The KT-BRST complex of a degenerate Lagrangian system

Quantization of a Lagrangian field system essentially depends on its degeneracy and implies its BRST extension defined by sets of non-trivial Noether and higher-stage Noether identities. However, one meets a problem how to select trivial and non-trivial higher-stage Noether identities. We show that, under certain conditions, one can associate to a degenerate Lagrangian L the KT-BRST complex of fields, antifields and ghosts whose boundary and coboundary operators provide all non-trivial Noether identities and gauge symmetries of L. In this case, L can be extended to a proper solution of the master equation.Comment: 15 pages, accepted for publication in Lett. Math. Phy

Subextensive singularity in the 2D ±J\pm J Ising spin glass

The statistics of low energy states of the 2D Ising spin glass with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le 48$, and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. The behavior of the density of states near the ground state energy is analyzed as a function of $L$, in order to obtain the low temperature behavior of the model. For large finite $L$ there is a range of $T$ in which the heat capacity is proportional to $T^{5.33 \pm 0.12}$. The range of $T$ in which this behavior occurs scales slowly to $T = 0$ as $L$ increases. Similar results are found for $p$ = 0.25. Our results indicate that this model probably obeys the ordinary hyperscaling relation $d \nu = 2 - \alpha$, even though $T_c = 0$. The existence of the subextensive behavior is attributed to long-range correlations between zero-energy domain walls, and evidence of such correlations is presented.Comment: 13 pages, 7 figures; final version, to appear in J. Stat. Phy

Power-law correlated phase in random-field XY models and randomly pinned charge-density waves

Monte Carlo simulations have been used to study the Z6 ferromagnet in a random field on simple cubic lattices, which is a simple model for randomly pinned charge-density waves. The random field is chosen to have infinite strength on a fraction x of the sites of the lattice, and to be zero on the remaining sites. For x= 1/16 there are two phase transitions. At low temperature there is a ferromagnetic phase, which is stabilized by the six-fold nonrandom anisotropy. The intermediate temperature phase is characterized by a |k|^(-3) decay of two-spin correlations, but no true ferromagnetic order. At the transition between the power-law correlated phase and the paramagnetic phase the magnetic susceptibility diverges, and the two-spin correlations decay approximately as |k|^(-2.87).Comment: 16 pages, 8 figures, Postscrip

Quantifying Self-Organization with Optimal Predictors

Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we propose a new criterion, namely an internally-generated increase in the statistical complexity, the amount of information required for optimal prediction of the system's dynamics. We precisely define this complexity for spatially-extended dynamical systems, using the probabilistic ideas of mutual information and minimal sufficient statistics. This leads to a general method for predicting such systems, and a simple algorithm for estimating statistical complexity. The results of applying this algorithm to a class of models of excitable media (cyclic cellular automata) strongly support our proposal.Comment: Four pages, two color figure

Quasi-long range order in the random anisotropy Heisenberg model

The large distance behaviors of the random field and random anisotropy Heisenberg models are studied with the functional renormalization group in $4-\epsilon$ dimensions. The random anisotropy model is found to have a phase with the infinite correlation radius at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law $<{\bf m}({\bf r}_1) {\bf m}({\bf r}_2)>\sim| {\bf r}_1-{\bf r}_2|^{-0.62\epsilon}$. The magnetic susceptibility diverges at low fields as $\chi\sim H^{-1+0.15\epsilon}$. In the random field model the correlation radius is found to be finite at the arbitrarily weak disorder.Comment: 4 pages, REVTe

Disorder Averaging and Finite Size Scaling

We propose a new picture of the renormalization group (RG) approach in the presence of disorder, which considers the RG trajectories of each random sample (realization) separately instead of the usual renormalization of the averaged free energy. The main consequence of the theory is that the average over randomness has to be taken after finding the critical point of each realization. To demonstrate these concepts, we study the finite-size scaling properties of the two-dimensional random-bond Ising model. We find that most of the previously observed finite-size corrections are due to the sample-to-sample fluctuation of the critical temperature and scaling is more adequate in terms of the new scaling variables.Comment: 4 pages, 6 figures include