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A modified three-dimensional mean spherical model with a L-layer film geometry under Neumann-Neumann boundary conditions is considered. Two spherical fields are present in the model: a surface one fixes the mean square value of the spins at the boundaries at some $rho > 0$, and a bulk one imposes the standard spherical constraint (the mean square value of the spins in the bulk equals one). The surface susceptibility $chi_{1,1}$ has been evaluated exactly. For $rho =1$ we find that $chi_{1,1}$ is finite at the bulk critical temperature $T_c$, in contrast with the recently derived value $gamma_{1,1}=1$ in the case of just one global spherical constraint. The result $gamma_{1,1}=1$ is recovered only if $rho =rho_c= 2-(12 K_c)^{-1}$, where $K_c$ is the dimensionless critical coupling. When $rho > rho_c$, $chi_{1,1}$ diverges exponentially as $Tto T_c^{+}$. An effective hamiltonian which leads to an exactly solvable model with $gamma_{1,1}=2$, the value for the $nto infty $ limit of the corresponding O(n) model, is proposed too.
We discuss universal and non-universal critical exponents of a three dimensional Ising system in the presence of weak quenched disorder. Both experimental, computational, and theoretical results are reviewed. Special attention is paid to the results
The massive field-theory approach for studying critical behavior in fixed space dimensions $d<4$ is extended to systems with surfaces.This enables one to study surface critical behavior directly in dimensions $d<4$ without having to resort to the $ep
We provide general formulae for the configurational exponents of an arbitrary polymer network connected to the surface of an arbitrary wedge of the two-dimensional plane, where the surface is allowed to assume a general mixture of boundary conditions
We present mathematical details of derivation of the critical exponents for the free energy and magnetization in the vicinity of the Gaussian fixed point of renormalization. We treat the problem in general terms and do not refer to particular models
The paramagnetic-to-ferromagnetic phase transition is believed to proceed through a critical point, at which power laws and scaling invariance, associated with the existence of one diverging characteristic length scale -- the so called correlation le