182 research outputs found
Correlation Inequalities for Spin Glasses
We prove a correlation type inequality for spin systems with quenched
symmetric random interactions. This gives monotonicity of the pressure with
respect to the strength of the interaction for a class of spin glass models.
Consequences include existence of the thermodynamic limit for the pressure and
bounds on the surface pressure. We also describe other conjectured inequalities
for such systems
Note on a diffraction-amplification problem
We investigate the solution of the equation \partial_t E(x,t)-iD\partial_x^2
E(x,t)= \lambda |S(x,t)|^2 E(x,t)$, for x in a circle and S(x,t) a Gaussian
stochastic field with a covariance of a particular form. It is shown that the
coupling \lambda_c at which diverges for t>=1 (in suitable units), is
always less or equal for D>0 than D=0.Comment: REVTeX file, 8 pages, submitted to Journal of Physics
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