Criticality in the two-dimensional random-bond Ising model

The two-dimensional (2D) random-bond Ising model has a novel multicritical point on the ferromagnetic to paramagnetic phase boundary. This random phase transition is one of the simplest examples of a 2D critical point occurring at both finite temperatures and disorder strength. We study the associated critical properties, by mapping the random 2D Ising model onto a network model. The model closely resembles network models of quantum Hall plateau transitions, but has different symmetries. Numerical transfer matrix calculations enable us to obtain estimates for the critical exponents at the random Ising phase transition. The values are consistent with recent estimates obtained from high-temperature series.Comment: minor changes, 7 pages LaTex, 8 postscript figures included using epsf; to be published Phys. Rev. B 55 (1997

Gauge Theory for Quantum Spin Glasses

The gauge theory for random spin systems is extended to quantum spin glasses to derive a number of exact and/or rigorous results. The transverse Ising model and the quantum gauge glass are shown to be gauge invariant. For these models, an identity is proved that the expectation value of the gauge invariant operator in the ferromagnetic limit is equal to the one in the classical equilibrium state on the Nishimori line. As a result, a set of inequalities for the correlation function are proved, which restrict the location of the ordered phase. It is also proved that there is no long-range order in the two-dimensional quantum gauge glass in the ground state. The phase diagram for the quantum XY Mattis model is determined.Comment: 15 pages, 2 figure

Aging Relation for Ising Spin Glasses

We derive a rigorous dynamical relation on aging phenomena -- the aging relation -- for Ising spin glasses using the method of gauge transformation. The waiting-time dependence of the auto-correlation function in the zero-field-cooling process is equivalent with that in the field-quenching process. There is no aging on the Nishimori line; this reveals arguments for dynamical properties of the Griffiths phase and the mixed phase. The present method can be applied to other gauge-symmetric models such as the XY gauge glass.Comment: 9 pages, RevTeX, 2 postscript figure

Non-equilibrium Relations for Spin Glasses with Gauge Symmetry

We study the applications of non-equilibrium relations such as the Jarzynski equality and fluctuation theorem to spin glasses with gauge symmetry. It is shown that the exponentiated free-energy difference appearing in the Jarzynski equality reduces to a simple analytic function written explicitly in terms of the initial and final temperatures if the temperature satisfies a certain condition related to gauge symmetry. This result is used to derive a lower bound on the work done during the non-equilibrium process of temperature change. We also prove identities relating equilibrium and non-equilibrium quantities. These identities suggest a method to evaluate equilibrium quantities from non-equilibrium computations, which may be useful to avoid the problem of slow relaxation in spin glasses.Comment: 8 pages, 2 figures, submitted to JPS

The Membrane Components of Crustacean Neuromuscular Systems.: II. Analysis of interactions among the electrogenic components

The present work provides additional evidence for the occurrence of a number of electrogenic components in crustacean and particularly crayfish muscle fibers. It demonstrates that these different components are independent. One or another can be eliminated or modified by various procedures without affecting the rest. However, interactions can occur between the different components. The coupling may be effected by the changes in membrane potential which result from changes in ionic permeabilities or by changes in the membrane conductance. Some interactions of such couplings which can perturb electrophysiological measurements are described and analyzed

The Membrane Components of Crustacean Neuromuscular Systems: I. Immunity of different electrogenic components to tetrodotoxin and saxitoxin

Axon spikes in crayfish and lobster neuromuscular preparations were blocked by tetrodotoxin or saxitoxin (concentration 10−9 to 10−8 g/ml). Responses evoked in the excitatory synaptic membrane by ionophoretically applied glutamate, or in the inhibitory by GABA were unaffected by concentrations of the poisons up to 10−5 g/ml. These confirm other findings that the poisons do not affect electrically inexcitable membrane components. “Miniature” p.s.p.’s, which indicate local secretory activity in the presynaptic terminals were unaffected by the poisons. Electrical stimuli applied to the axon terminals elicited localized p.s.p.’s after spike electrogenesis of the axons was blocked. Thus, persistence of secretory activity may be linked to persistence of depolarizing K activation in the axons. Spikes induced in the muscle fibers by procaine were not affected by the poisons. In correlation with other data this finding indicates that the depolarizing electrogenic element, which does not depend upon Na activation in the normally gradedly responsive muscles, differs chemically from the Na activation component which is present in the conductile membrane of various cells. Three other varieties of electrically excitable response which are present in crayfish muscle fibers (hyperpolarizing Cl activation, depolarizing K inactivation, and K activation) were, likewise, immune to the toxin

Random Fixed Point of Three-Dimensional Random-Bond Ising Models

The fixed-point structure of three-dimensional bond-disordered Ising models is investigated using the numerical domain-wall renormalization-group method. It is found that, in the +/-J Ising model, there exists a non-trivial fixed point along the phase boundary between the paramagnetic and ferromagnetic phases. The fixed-point Hamiltonian of the +/-J model numerically coincides with that of the unfrustrated random Ising models, strongly suggesting that both belong to the same universality class. Another fixed point corresponding to the multicritical point is also found in the +/-J model. Critical properties associated with the fixed point are qualitatively consistent with theoretical predictions.Comment: 4 pages, 5 figures, to be published in Journal of the Physical Society of Japa

Nishimori point in the 2D +/- J random-bond Ising model

We study the universality class of the Nishimori point in the 2D +/- J random-bond Ising model by means of the numerical transfer-matrix method. Using the domain-wall free-energy, we locate the position of the fixed point along the Nishimori line at the critical concentration value p_c = 0.1094 +/- 0.0002 and estimate nu = 1.33 +/- 0.03. Then, we obtain the exponents for the moments of the spin-spin correlation functions as well as the value for the central charge c = 0.464 +/- 0.004. The main qualitative result is the fact that percolation is now excluded as a candidate for describing the universality class of this fixed point.Comment: 4 pages REVTeX, 3 PostScript figures; final version to appear in Phys. Rev. Lett.; several small changes and extended explanation

Nishimori point in random-bond Ising and Potts models in 2D

We study the universality class of the fixed points of the 2D random bond q-state Potts model by means of numerical transfer matrix methods. In particular, we determine the critical exponents associated with the fixed point on the Nishimori line. Precise measurements show that the universality class of this fixed point is inconsistent with percolation on Potts clusters for q=2, corresponding to the Ising model, and q=3Comment: 11 pages, 3 figures. Contribution to the proceedings of the NATO Advanced Research Workshop on Statistical Field Theories, Como 18-23 June 200