We analyze the high-temperature conductivity in one-dimensional integrable models of interacting fermions: the t-V model (anisotropic Heisenberg spin chain) and the Hubbard model, at half-filling in the regime corresponding to insulating ground state. A microcanonical Lanczos method study for finite size systems reveals anomalously large finite-size effects at low frequencies while a frequency-moment analysis indicates a finite d.c. conductivity. This phenomenon also appears in a prototype integrable quantum system of impenetrable particles, representing a strong-coupling limit of both models. In the thermodynamic limit, the two results could converge to a finite d.c. conductivity rather than an ideal conductor or insulator scenario.

We show how to generalize the zero-temperature Lanczos method for calculating dynamical correlation functions to finite temperatures. The key is the microcanonical ensemble which allows us to replace the involved canonical ensemble with a single appropriately chosen state; in the thermodynamic limit it provides the same physics as the canonical ensemble but with the evaluation of a single expectation value. We can employ the same system sizes as for zero temperature but, whereas the statistical fluctuations present in small systems are prohibitive, the spectra of the largest system sizes are surprisingly smooth. We investigate, as a test case, the spin conductivity of the spin-1/2 anisotropic Heisenberg model and in particular we present a comparison of spectra obtained by the canonical and microcanonical ensemble methods.

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We study the electron spin resonance of low-dimensional spin systems at high temperature and test the Kubo-Tomita theory of exchange narrowing. In finite-size systems ͑molecular magnets͒, we found a doublepeak resonance which strongly differs from the usual Lorentzian. For infinite systems, we have predictions for the linewidth and line shape as a function of the anisotropy strength. For this, we have used an interpolation between a nonperturbative calculation of the memory function at short times ͑exact diagonalization͒ and the hydrodynamic spin diffusion at long times. We show that the Dzyaloshinskii-Moriya anisotropies generally induce a much larger linewidth than the exchange anisotropies in two dimensions, contrary to the onedimensional case.

Two dimensional suspensions of spherical colloids subject to periodic external fields exhibit a rich variety of molecular crystalline phases. We study in simulations the ground state configurations of dimeric and trimeric systems, that are realized on square and triangular lattices, when either two or three macroions are trapped in each external potential minimum. Bipartite orders of the checkerboard or stripe types are reported together with more complex quadripartite orderings, and the shortcomings of envisioning the colloids gathered in a single potential minimum as a composite rigid object are discussed. This work also sheds light on simplifying assumptions underlying previous theoretical treatments and that made possible the mapping onto spin models.