  We consider the problem of signal estimation (denoising) from a
statistical-mechanical perspective, in continuation to a recent work on the
analysis of mean-square error (MSE) estimation using a direct relationship
between optimum estimation and certain partition functions. The paper consists
of essentially two parts. In the first part, using the aforementioned
relationship, we derive single-letter expressions of the mismatched MSE of a
codeword (from a randomly selected code), corrupted by a Gaussian vector
channel. In the second part, we provide several examples to demonstrate phase
transitions in the behavior of the MSE. These examples enable us to understand
more deeply and to gather intuition regarding the roles of the real and the
mismatched probability measures in creating these phase transitions.
