We study numerically, using a one-dimensional Heisenberg model, the spin-Peierls transition in the linear Cu 2+ spin-1/2 chains in the inorganic compound CuGeO 3 which has been recently observed experimentally. We suggest that the magnetic susceptibility, the temperature dependence of the spin gap and the spin-Peierls transition temperature of this material can be reasonably described by including nearest and next nearest neighbor antiferromagnetic interactions along the chain. We estimate that the nearest neighbor exchange parameter J is approximately 160 K, and that the next nearest neighbor exchange parameter is approximately 0.36 J.

The microscopic mechanism of the melting of a crystal is analyzed by the constant pressure Monte Carlo simulation of a Lennard-Jones fcc system. Beyond a temperature of the order of 0.8 of the melting temperature, we found that the relevant excitations are lines of defects. Each of these lines has the structure of a random walk of various lengths on an fcc defect lattice. We identify these lines with the dislocation ones proposed in recent phenomenological theories of melting. Near melting we find the appearance of long lines that cross the whole system. We suggest that these long lines are the precursor of the melting process. : 64.70.Dv, 61.72.Bd, Melting is one of the rare phase transitions that can be observed in real life, outside of laboratories. Being a common-life process, the melting mechanism has been of interest for centuries. However there is yet no complete understanding of the atomistic dynamics involved in the melting transition. This is due to several difficulties found both in the experimental and theoretical studies of this problem. Let us discuss some of these difficulties. PACSUpon a phase transition long-range order found in the low temperature phase (LTP) disappears at the transition temperature. In the simplest cases, such as a structural phase transition, order is associated with a geometrical quantity which distinguishes LTP from the high temperature phase (HTP). The dynamical collective structural deformation, namely phonons, converting LTP into HTP is already present in the higher-symmetry phase. It is therefore natural to assume that the softening of this phonon excitation is the essential mechanism of the phase transition capturing the most important dynamics of the particles near the transition point.However, at the melting temperature T m , both translational and rotational symmetries of a crystal are destroyed, and it is much more complicated to construct simple models including the relevant excitations on both sides of the transition temperature. Hence, one-phase models have been developed. Starting in the solid phase, the question is what kind of excitation could destroy crystalline order. It is easy to see [1] that phonons alone cannot convert a solid into a liquid, some kind of crystalline defects should be invoked. Kosterlitz and Thouless [2] proposed a fundamental theory of the thermal breakdown of long-range order in two dimensions (2D) by topological defects, and related it to transitions in 2D crystals, superfluids and magnets, the relevant topological defects in the case of melting being crystalline dislocations (which are point defects in 2D). Their theory was greatly extended and detailed by Halperin and Nelson [3] and Yound [4] who predicted that the complete transition from solid to liquid takes place in two steps: the dissociation of dislocation pairs drives a crystal into a liquid-crystal phase that retains finite-range orientational order, then a second transition at higher temperature completes the conversion to an isotropic liquid. This complete theory gave det...