We present a systematic investigation of the distribution of normal forces at the boundaries of static packings of spheres. A method for the efficient construction of large hexagonal-close-packed crystals is introduced and used to study the effect of spatial ordering on the distribution of forces. Under uniaxial compression we find that the form for the probability distribution of normal forces between particles does not depend strongly on crystallinity or interparticle friction. In all cases the distribution decays exponentially at large forces and shows a plateau or possibly a small peak near the average force but does not tend to zero at small forces.

We study a two-dimensional compressible Ising spin glass at constant volume. The spin interactions are coupled to the distance between neighboring particles in the Edwards-Anderson model with ±J interactions. We find that the energy of a given spin configuration is shifted from its incompressible value, E0, by an amount quadratic in E0 and proportional to the coupling strength. We then construct a simple model expressed only in terms of spin variables that predicts the existence of a critical value of the coupling above which the spin-glass transition disappears.PACS numbers: 75.10. Nr,75.40.Mg,05.50.+q Lattice compressibility affects the nature of phase transitions in a variety of spin systems. The 2-dimensional (2-D) triangular Ising antiferromagnet, for example, is fully frustrated and shows no transition to an ordered state; however, when compressibility is added, this system exhibits a first-order transition to a striped phase [1,2]. In the (unfrustrated) Ising ferromagnet, the introduction of compressibility changes the transition from second-to first-order so that the onset of nonzero net magnetization is simultaneous with a discontinuous change in the volume [3,4]. Frustration is central to the nature of the spin-glass transition as it leads to large ground-state degeneracies [5,6,7,8]. Because different states with the same spin-glass energy can couple differently to local lattice deformations, compressibility lifts the ground-state degeneracy and may dramatically alter the nature of the transition and the low-temperature spin-glass phase. Since magneto-elastic effects are always present to some degree in physical systems, their inclusion in spin-glass models may help explain some of the outstanding puzzles in spin-glass experiments [9]. We report here the effect of compressibility on a 2-D spin glass in which the lattice is allowed to distort locally while the entire system is held at constant volume.The ground states of the previously studied compressible systems were always states that had already been ground states of those same systems without lattice distortion. In contrast, we find that as the coupling between magnetic interactions and lattice distortions is increased, the constant-volume compressible spin glass prefers spin configurations which had previously been excited states. We further find that the critical region just above the spin-glass temperature is suppressed as the coupling to lattice distortions increases so that above a certain value of the coupling, the spin-glass transition is eliminated entirely.We study compressible two-dimensional Ising spin glasses on square lattices with periodic boundary conditions at constant volume. The Hamiltonian isThe first term is the energy of the standard (incompressible) Edwards-Anderson spin glass, with a sum over nearest neighbors. The spins S i take the values ±1, and J ij ∈ {±J}. The second term couples the spin interactions to local lattice distortions; r ij is the distance between particles i and j, and r 0 is the particle separation of t...

Numerical studies of a compressible version of the Ising spin glass in two dimensions are reported. Compressibility is introduced by adding a term that couples the spin-spin interactions and local lattice deformations to the standard Edwards-Anderson model. The relative strength of this coupling is controlled by a single dimensionless parameter . The time scale associated with the dynamics of the system grows exponentially as is increased, and the energy of the compressible system is shifted downward by an amount proportional to times the square of the uncoupled energy. This result leads to the formulation of a simplified model that depends solely on spin variables; analysis and numerical simulations of the simplified model predict a critical value of the coupling strength above which the spin-glass transition cannot exist at any temperature.

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