Detailed balancing approach to disordered copolymeric Ising chains

Abstract

The problem of disordered copolymeric one‐dimensional Ising chains with nearest‐neighbor interactions is formulated in full generality, using the principle of detailed balancing. The natural variables in this theory are a set of nearest‐neighbor conditional probabilities and singlets. A set of coupled nonlinear difference equations in these variables is derived, which completely determine the state of the chain with respect to both composition and fine structure. A special but nontrivial case of the general model is treated in detail to illustrate the theory and to make possible comparisons with the work of others. The problem of the strictly alternating copolymer is readily solved by way of illustration. An efficient and accurate numerical approach, employing a Monte Carlo technique, is used to evaluate these equations for disordered chains, both random and nonrandom. Example calculations, based on data for a binary RNA, show the doublet variables to be more sensitive to differences between random and nonrandom chains than the singlets. Triplet and higher configurational probabilities can also be readily calculated. The numerical computations make it clear that our results are equivalent to ensemble average results given by Lehman and McTague who numerically evaluate integral and functional equations for the logarithm of the partition function.