  A spin system can be thought of as an information coding system that
transfers information of the interaction configuration into information of the
equilibrium state of the spin variables. Hence it can be expected that the
relations between the interaction configuration and equilibrium states are
consistent with the known laws of information theory. We show that Shannon's
rate-distortion theorem can be used to obtain an universal constraint on
neighboring spin correlations for a broad range of Ising spin systems with
two-body spin interactions. Remarkably, this constraint gives a bound for the
multicritical point in the phase diagram, when a mean-field behavior for the
neighboring spin pairs can be expected in the paramagnetic phase.
