The two-dimensional J-J' dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio alpha=J'/J. The critical point of the order-disorder quantum phase transition in the J-J' model is determined as alpha_c=2.5196(2) by finite-size scaling for up to approximately 10 000 quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the J-J' model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.

Using state of the art Monte Carlo simulations of a bead-spring model we investigate both the equilibrium and the nonequilibrium behavior of the homopolymer collapse. The equilibrium properties obtained via multicanonical sampling recover the well-known finite-size scaling behavior of collapse for our model polymer. For the nonequilibrium dynamics we study the collapse by quenching the homopolymer from an expanded coiled state into the globular phase. The sequence of events observed during the collapse is independent of the quench depth. In particular, we focus on finding out universal scaling behaviors related to the growth or coarsening of clusters of monomers, by drawing phenomenological analogies with ordering kinetics. We distinguish the cluster coarsening stage from the initial stage of primary cluster formation. By successful application of a nonequilibrium finite-size scaling analysis we show that at all quench temperatures, during the coarsening stage, the cluster growth is roughly linear and can be characterised by a universal finite-size scaling function. In addition, we provide evidence of aging by constructing a suitable autocorrelation function and its corresponding dynamical power-law scaling with respect to the growing cluster sizes. The predicted theoretical bound for the exponent governing such scaling is strictly obeyed by the numerical data irrespective of the quench temperature. The results and methods presented here in general should find application in similar phenomena such as the collapse of a protein molecule preceding its folding.

We present a temperature-independent Monte Carlo method for the determination of the density of states of lattice proteins that combines the fast ground-state search strategy of the nPERM chain growth and multicanonical reweighting for sampling the complete energy space. Since the density of states contains all energetic information of a statistical system, we can directly calculate the mean energy, specific heat, Gibbs free energy, and entropy for all temperatures. We apply this method to HP lattice proteins and for the examples of sequences considered, we identify the transitions between native, globule, and random coil states. Since no special properties of heteropolymers are involved in this algorithm, the method applies to polymer models as well.The simulation of protein folding is extremely challenging, since the interactions between the constituents of the macromolecule and the influence of the environment require sophisticated models. One of the most essential aspects in the description of the folding process is the formation of a compact core of hydrophobic amino acid residues (H) which is screened from water by hydrophilic or polar residues (P). This characteristic property of realistic proteins can be qualitatively studied with simple lattice models such as the HP model [1]. By taking into account the attractive interaction between hydrophobic monomers only, the energy of a lattice protein with certain conformation and sequence is calculated as follows:where i, j < i − 1 symbolises that the sum is taken only over nearest lattice neighbours being nonadjacent along the self-avoiding chain of monomers. If the ith monomer is hydrophobic, σ i = 1, while for a polar monomer σ i = 0.As it is one of the main goals in off-lattice simulations to find low-lying energy states within a rough free energy landscape, good lattice folders are expected to have lowdegenerated ground states. Much work has been done on identifying designing sequences with such native states. Ground-state search strategies on three-dimensional lattices range, for example, from enumeration [2,3] over hydrophobic core construction [4,5] and contact interaction [6] to chain growth methods [7][8][9][10]. Low-lying energy states for HP sequences with up to 136 monomers were identified with these methods. *

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