By Sylvester J.J.

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In Sec. 3 we have obtained Yang-Lee zeros for classical picture of hydrogen bond between N - H . O = C of helix-coil phase transition for polypeptides and pro- aTalk presented by N. S. A. at the XIth Regional Conference on Mathematical Physics, May 2004, Tehran, Iran. 22 teins in thermodynamic limit on recursive zigzag ladder. In Sec. 4 we have obtained Arnold tongues for non-classical helix-coil phase transition. 25 0 . 5 0 . 7 5 Let us regard the anti-ferromagnetic Ising and Potts models on the recursive Bethe lattice connected through sites.

The answer to this question was given in 1952 by Lee and Yang in their seminal papers1. It was shown that phase transitions occur in the systems in which the continuous distribution of zeros of the partition function intersects the real axis in the thermodynamic limit. For anti-ferromagnetic Potts models, by contrast, there are some tantalizing conjectures concerning the critical loci, but many aspects still remain obscure2. It is interesting to regard the line between paramagnetic and modulated phases.

The source of complexity is the above mentioned factorization of N-particle scattering matrix, which in these case restricts the two-particle S-matrices to satisfy some kind of spectral Yang-Baxter (SYB) equation. Here, we are going to study the most general multi-species model, i. e. the most general boundary condition, where all the previous known models are the special cases of it. In its general form, the reactions are A,0 A,Ap + 0A, + A,As with rate 1 , with rate c$, A,Ap@ + 8A,A6 with rate b;f, where the dots indicate the other drop-push reactions with n adjacent particles, in which in the meantime the types of the particles can also be changed.

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The Collected Mathematical Papers, Volume II by Sylvester J.J.

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