Random-field spin models beyond 1 loop: a mechanism for decreasing the lower critical dimension

The functional renormalization group for the random-field and random-anisotropy O(N) sigma models is studied to 2 loop. The ferromagnetic-disordered (F-D) transition fixed point is found to next order in d = 4 + epsilon for N > N(c) (N(c) = 2.834 740 8 for random field, N(c) = 9.441 21 for random anisotropy). For N < N(c) the lower critical dimension d = d(lc) plunges below d(lc) = 4: we find two fixed points, one describing the quasiordered phase, the other is novel and describes the F-D transition. d(lc) can be obtained in an (N(c)-N) expansion. The theory is also analyzed at large N and a glassy regime is found.     

Dynamics of Ising spin glasses far below the lower critical dimension: The one-dimensional case and small clusters

The Glauber model is studied for symmetric distributions (±J and gaussian) of the nearest-neighbour interactionJ, including a magnetic field. For small clusters of spins (closed rings ofN bonds, withN7) the complex magnetic susceptibility () and the time-dependent remanent magnetizationm(t) are found exactly for given bond configurations {J _ij } by diagonalization of the Liouville operator; apart from the ±J model, the average over {J _ij } must be done numerically by simple random sampling Monte Carlo. Nevertheless our accuracy is much better than corresponding dynamic Monte Carlo simulations, even if one considers the extrapolation toN.We analyze the results along the lines of corresponding experimental work, studying the frequency-dependence of the peak in (), theT lnt-scaling ofm(t) at low temperaturesT, and the decomposition of () into a spectrum of relaxation times. Many results are strikingly similar to experimental data for systems such as the Holmium-Borate spinglass or the superparamagnet Eu_0.05Sr_0.95S, for instance. Frequency-dependent critical fieldsH _c () in theH-T plane are also identified but do not have the familiar Almeida-Thouless shape, however.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Polyakov loop and spin correlators on finite lattices A study beyond the mass gap

We derive an analytic expression for point-to-point correlation functions of the Polyakov loop based on the transfer matrix formalism. For the 21) Ising model we show that the results deduced from point-point spin correlators are coinciding with those from zero momentum correlators. We investigate the contributions from eigenvalues of the transfer matrix beyond the mass gap and discuss the limitations and possibilities of such an analysis. The finite size behaviour of the obtained 21) Ising model matrix elements is examined. The point-to-point correlator formula is then applied to Polyakov loop data in finite temperature SU(2) gauge theory. The leading matrix element shows all expected scaling properties. Just above the critical point we find a Debye screening mass μ_D/T ≈ 4 , independent of the volume.