Correlation Functions of Multisite Interaction Spin-S models on the Bethe-like Lattices

Multisite interaction spin-S models in an external magnetic field are studied recursively on the Bethe-like lattices. The transfer-matrix method is extended to calculate exactly the two-spin correlation functions. The exact expressions for the correlation length and magnetic susceptibility are derived for spin-1/2 models. The singularity of the correlation length with critical index $\nu =1$ and the proportionality of magnetic susceptibility to correlation length in the second order phase transition region of spin-1/2 ferromagnetic models on the Bethe-like lattices are established analytically.Comment: 13 pages, In Press Int. J. Mod. Phys.

Universal geometrical factor of protein conformations as a consequence of energy minimization

The biological activity and functional specificity of proteins depend on their native three-dimensional structures determined by inter- and intra-molecular interactions. In this paper, we investigate the geometrical factor of protein conformation as a consequence of energy minimization in protein folding. Folding simulations of 10 polypeptides with chain length ranging from 183 to 548 residues manifest that the dimensionless ratio (V/(A)) of the van der Waals volume V to the surface area A and average atomic radius of the folded structures, calculated with atomic radii setting used in SMMP [Eisenmenger F., et. al., Comput. Phys. Commun., 138 (2001) 192], approach 0.49 quickly during the course of energy minimization. A large scale analysis of protein structures show that the ratio for real and well-designed proteins is universal and equal to 0.491\pm0.005. The fractional composition of hydrophobic and hydrophilic residues does not affect the ratio substantially. The ratio also holds for intrinsically disordered proteins, while it ceases to be universal for polypeptides with bad folding properties.Comment: 6 pages, 1 table, 4 figure

Classical phase transitions in a one-dimensional short-range spin model

Ising's solution of a classical spin model famously demonstrated the absence of a positive-temperature phase transition in one-dimensional equilibrium systems with short-range interactions. No-go arguments established that the energy cost to insert domain walls in such systems is outweighed by entropy excess so that symmetry cannot be spontaneously broken. An archetypal way around the no-go theorems is to augment interaction energy by increasing the range of interaction. Here we introduce new ways around the no-go theorems by investigating entropy depletion instead. We implement this for the Potts model with invisible states.Because spins in such a state do not interact with their surroundings, they contribute to the entropy but not the interaction energy of the system. Reducing the number of invisible states to a negative value decreases the entropy by an amount sufficient to induce a positive-temperature classical phase transition. This approach is complementary to the long-range interaction mechanism. Alternatively, subjecting positive numbers of invisible states to imaginary or complex fields can trigger such a phase transition. We also discuss potential physical realisability of such systems.Comment: 29 pages, 11 figure

Yang-Lee Zeros of the Q-state Potts Model on Recursive Lattices

The Yang-Lee zeros of the Q-state Potts model on recursive lattices are studied for non-integer values of Q. Considering 1D lattice as a Bethe lattice with coordination number equal to two, the location of Yang-Lee zeros of 1D ferromagnetic and antiferromagnetic Potts models is completely analyzed in terms of neutral periodical points. Three different regimes for Yang-Lee zeros are found for Q>1 and 0<Q<1. An exact analytical formula for the equation of phase transition points is derived for the 1D case. It is shown that Yang-Lee zeros of the Q-state Potts model on a Bethe lattice are located on arcs of circles with the radius depending on Q and temperature for Q>1. Complex magnetic field metastability regions are studied for the Q>1 and 0<Q<1 cases. The Yang-Lee edge singularity exponents are calculated for both 1D and Bethe lattice Potts models. The dynamics of metastability regions for different values of Q is studied numerically.Comment: 15 pages, 6 figures, with correction