Chiral mixed phase in disordered 3d Heisenberg models

Using Monte Carlo simulations, we compute the spin stiffness of a site-random 3d Heisenberg model with competing ferromagnetic and antiferromagnetic interactions. Our results for the pure limit yield values of the the critical temperature and the critical exponent $\nu$ in excellent agreement with previous high precision studies. In the disordered case, a mixed "chiral" phase is found which may be in the same universality class as 3d Heisenberg spin glasses.Comment: 5 pages, 4 figures, accepted in PRB Rapid Communication

Phase glass and zero-temperature phase transition in a randomly frustrated two-dimensional quantum rotor model

The ground state of the quantum rotor model in two dimensions with random phase frustration is investigated. Extensive Monte Carlo simulations are performed on the corresponding (2+1)-dimensional classical model under the entropic sampling scheme. For weak quantum fluctuation, the system is found to be in a phase glass phase characterized by a finite compressibility and a finite value for the Edwards-Anderson order parameter, signifying long-ranged phase rigidity in both spatial and imaginary time directions. Scaling properties of the model near the transition to the gapped, Mott insulator state with vanishing compressibility are analyzed. At the quantum critical point, the dynamic exponent $z_{\rm dyn}\simeq 1.17$ is greater than one. Correlation length exponents in the spatial and imaginary time directions are given by $\nu\simeq 0.73$ and $\nu_z\simeq 0.85$, respectively, both assume values greater than 0.6723 of the pure case. We speculate that the phase glass phase is superconducting rather than metallic in the zero current limit.Comment: 14 pages, 4 figures, to appear in JSTA

Spin Gap in Two-Dimensional Heisenberg Model for CaV4_4O9_9

We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV$_4$O$_9$. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.Comment: 8 pages, 6 figures available upon request (Revtex

Phase Transition in the Two-Dimensional Gauge Glass

The two-dimensional XY gauge glass, which describes disordered superconducting grains in strong magnetic fields, is investigated, with regard to the possibility of a glass transition. We compute the glass susceptibility and the correlation function of the system via extensive numerical simulations and perform the finite-size scaling analysis. This gives strong evidence for a finite-temperature transition, which is expected to be of a novel type.Comment: 5pages, 3 figures, revtex, to appear in Phys. Rev.

Temperature behavior of the magnon modes of the square lattice antiferromagnet

A spin-wave theory of short-range order in the square lattice Heisenberg antiferromagnet is formulated. With growing temperature from T=0 a gapless mode is shown to arise simultaneously with opening a gap in the conventional spin-wave mode. The spectral intensity is redistributed from the latter mode to the former. For low temperatures the theory reproduces results of the modified spin-wave theory by M.Takahashi, J.E.Hirsch et al. and without fitting parameters gives values of observables in good agreement with Monte Carlo results in the temperature range 0 <= T < 0.8J where J is the exchange constant.Comment: 12 pages, 2 figure

Two spin liquid phases in the spatially anisotropic triangular Heisenberg model

The quantum spin-1/2 antiferromagnetic Heisenberg model on a two dimensional triangular lattice geometry with spatial anisotropy is relevant to describe materials like ${\rm Cs_2 Cu Cl_4}$ and organic compounds like {$\kappa$-(ET)$_2$Cu$_2$(CN)$_3$}. The strength of the spatial anisotropy can increase quantum fluctuations and can destabilize the magnetically ordered state leading to non conventional spin liquid phases. In order to understand these intriguing phenomena, quantum Monte Carlo methods are used to study this model system as a function of the anisotropic strength, represented by the ratio $J'/J$ between the intra-chain nearest neighbor coupling $J$ and the inter-chain one $J'$. We have found evidence of two spin liquid regions. The first one is stable for small values of the coupling J'/J \alt 0.65, and appears gapless and fractionalized, whereas the second one is a more conventional spin liquid with a small spin gap and is energetically favored in the region 0.65\alt J'/J \alt 0.8. We have also shown that in both spin liquid phases there is no evidence of broken translation symmetry with dimer or spin-Peirls order or any broken spatial reflection symmetry of the lattice. The various phases are in good agreement with the experimental findings, thus supporting the existence of spin liquid phases in two dimensional quantum spin-1/2 systems.Comment: 35 pages, 24 figures, 3 table

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

Evidence for the droplet/scaling picture of spin glasses

We have studied the Parisi overlap distribution for the three dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the full Parisi replica symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behaviour in Monte Carlo simulations is due to the fact that all existing simulations have been done at temperatures too close to the transition temperature so that sytem sizes larger than the correlation length have not been achieved.Comment: 4 pages, 6 figure

Fluctuation Dissipation Ratio in Three-Dimensional Spin Glasses

We present an analysis of the data on aging in the three-dimensional Edwards Anderson spin glass model with nearest neighbor interactions, which is well suited for the comparison with a recently developed dynamical mean field theory. We measure the parameter $x(q)$ describing the violation of the relation among correlation and response function implied by the fluctuation dissipation theorem.Comment: LaTeX 10 pages + 4 figures (appended as uuencoded compressed tar-file), THP81-9

Simulation Studies on the Stability of the Vortex-Glass Order

The stability of the three-dimensional vortex-glass order in random type-II superconductors with point disorder is investigated by equilibrium Monte Carlo simulations based on a lattice XY model with a uniform field threading the system. It is found that the vortex-glass order, which stably exists in the absence of screening, is destroyed by the screenng effect, corroborating the previous finding based on the spatially isotropic gauge-glass model. Estimated critical exponents, however, deviate considerably from the values reported for the gauge-glass model.Comment: Minor modifications made, a few referenced added; to appear in J. Phys. Soc. Jpn. Vol.69 No.1 (2000