Collapsing lattice animals and lattice trees in two dimensions

We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second order transitions from an extended to a collapsed phase in the resulting 2-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into two different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees, but the other is {\it not yet} bond driven and does not contain the Derrida-Herrmann model as special point. Instead it ends at a multicritical point $P^*$ where a transition line between two collapsed phases (one bond-driven and the other contact-driven) sparks off. The Derrida-Herrmann model is representative for the bond driven collapse, which then forms the fourth universality class on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime. Finally, it is very difficult to obtain with our method good estimates of the critical parameters of the Derrida-Herrmann universality class. As regards the bond-driven to contact-driven transition in the collapsed phase, we have some evidence for its existence and rough location, but no precise estimates of critical exponents.Comment: 11 pages, 16 figures, 1 tabl

Monte Carlo Procedure for Protein Design

A new method for sequence optimization in protein models is presented. The approach, which has inherited its basic philosophy from recent work by Deutsch and Kurosky [Phys. Rev. Lett. 76, 323 (1996)] by maximizing conditional probabilities rather than minimizing energy functions, is based upon a novel and very efficient multisequence Monte Carlo scheme. By construction, the method ensures that the designed sequences represent good folders thermodynamically. A bootstrap procedure for the sequence space search is devised making very large chains feasible. The algorithm is successfully explored on the two-dimensional HP model with chain lengths N=16, 18 and 32.Comment: 7 pages LaTeX, 4 Postscript figures; minor change

Design Equation: A Novel Approach to Heteropolymer Design

A novel approach to heteropolymer design is proposed. It is based on the criterion by Kurosky and Deutsch, with which the probability of a target conformation in a conformation space is maximized at low but finite temperature. The key feature of the proposed approach is the use of soft spins (fuzzy monomers) that leads to a design equation, which is an analog of the Boltzmann machine learning equation in the design problem. We implement an algorithm based on the design equation for the generalized HP model on the 3x3x3 cubic lattice and check its performance.Comment: 7 pages, 3 tables, 1 figures, uses jpsj.sty, jpsjbs1.sty, epsf.sty, Submitted to J. Phys. Soc. Jp

Protein design in a lattice model of hydrophobic and polar amino acids

A general strategy is described for finding which amino acid sequences have native states in a desired conformation (inverse design). The approach is used to design sequences of 48 hydrophobic and polar aminoacids on three-dimensional lattice structures. Previous studies employing a sequence-space Monte-Carlo technique resulted in the successful design of one sequence in ten attempts. The present work also entails the exploration of conformations that compete significantly with the target structure for being its ground state. The design procedure is successful in all the ten cases.Comment: RevTeX, 12 pages, 1 figur

Folding, Design and Determination of Interaction Potentials Using Off-Lattice Dynamics of Model Heteropolymers

We present the results of a self-consistent, unified molecular dynamics study of simple model heteropolymers in the continuum with emphasis on folding, sequence design and the determination of the interaction parameters of the effective potential between the amino acids from the knowledge of the native states of the designed sequences.Comment: 8 pages, 3 Postscript figures, uses RevTeX. Submitted to Physical Review Letter

Steric constraints in model proteins

A simple lattice model for proteins that allows for distinct sizes of the amino acids is presented. The model is found to lead to a significant number of conformations that are the unique ground state of one or more sequences or encodable. Furthermore, several of the encodable structures are highly designable and are the non-degenerate ground state of several sequences. Even though the native state conformations are typically compact, not all compact conformations are encodable. The incorporation of the hydrophobic and polar nature of amino acids further enhances the attractive features of the model.Comment: RevTex, 5 pages, 3 postscript figure

Equilibrium and dynamical properties of the ANNNI chain at the multiphase point

We study the equilibrium and dynamical properties of the ANNNI (axial next-nearest-neighbor Ising) chain at the multiphase point. An interesting property of the system is the macroscopic degeneracy of the ground state leading to finite zero-temperature entropy. In our equilibrium study we consider the effect of softening the spins. We show that the degeneracy of the ground state is lifted and there is a qualitative change in the low temperature behaviour of the system with a well defined low temperature peak of the specific heat that carries the thermodynamic ``weight'' of the ground state entropy. In our study of the dynamical properties, the stochastic Kawasaki dynamics is considered. The Fokker-Planck operator for the process corresponds to a quantum spin Hamiltonian similar to the Heisenberg ferromagnet but with constraints on allowed states. This leads to a number of differences in its properties which are obtained through exact numerical diagonalization, simulations and by obtaining various analytic bounds.Comment: 9 pages, RevTex, 6 figures (To appear in Phys. Rev. E

Hidden magnetic transitions in thermoelectric layered cobaltite, [Ca2_2CoO3_3]0.62_{0.62}[CoO2_2]

A positive muon spin rotation and relaxation ($\mu^+$SR) experiment on [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$], ({\sl i.e.}, Ca$_3$Co$_4$O$_9$, a layered thermoelectric cobaltite) indicates the existence of two magnetic transitions at $\sim$ 100 K and 400 - 600 K; the former is a transition from a paramagnetic state to an incommensurate ({\sf IC}) spin density wave ({\sf SDW}) state. The anisotropic behavior of zero-field $\mu^+$SR spectra at 5 K suggests that the {\sf IC-SDW} propagates in the $a$-$b$ plane, with oscillating moments directed along the c-axis; also the {\sf IC-SDW} is found to exist not in the [Ca$_2$CoO$_3$] subsystem but in the [CoO$_2$] subsystem. In addition, it is found that the long-range {\sf IC-SDW} order completes below $\sim$ 30 K, whereas the short-range order appears below 100 K. The latter transition is interpreted as a gradual change in the spin state of Co ions %% at temperatures above 400 K. These two magnetic transitions detected by $\mu^+$SR are found to correlate closely with the transport properties of [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$].Comment: 7 pages, 8 figures. to be appeared in Phys. Rev.

Two dimensional self-avoiding walk with hydrogen-like bonding: Phase diagram and critical behaviour

The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model displays a collapse transition. In contrast to the standard $\theta$-point model, the transition is first order. The phase diagram in the full fugacity-temperature plane displays an additional transition line, when compared to the $\theta$-point model, as well as a critical transition at finite temperature in the hamiltonian walk limit.Comment: 22 pages, 13 figures. To appear in Journal of Physics