We present spectral density reweighting techniques adapted to the analysis of a time series of data with a continuous range of allowed values. In a first application we analyze action and Polyakov line data from a Monte Carlo simulation on L t L 3 (L t = 2, 4) lattices for the SU(3) deconfining phase transition. We calculate partition function zeros, as well as maxima of the specific heat and of the order parameter susceptibility. Details and warnings are given concerning i) autocorrelations in computer time and ii) a reliable extraction of partition function † Submitted to Nuclear 1 zeros. The finite size scaling analysis of these data leads to precise results for the critical couplings β c , for the critical exponent ν and for the latent heat △s. In both cases (L t = 2 and 4), the first order nature of the transition is substantiated.

We report on multicanonical simulations of the helix-coil transition of a polypeptide. The nature of this transition was studied by calculating partition function zeros and the finite-size scaling of various quantities. New estimates for critical exponents are presented.87.15. He, 64.70Cn, 02.50.Ng A common, ordered structure in proteins is the α-helix and it is conjectured that formation of α-helices is a key factor in the early stages of protein-folding [1]. It is long known that α-helices undergo a sharp transition towards a random coil state when the temperature is increased. The characteristics of this so-called helix-coil transition have been studied extensively [2], most recently in Refs. [3,4]. They are usually described in the framework of Zimm-Bragg-type theories [5] in which the homopolymers are approximated by a one-dimensional Ising model with the residues as "spins" taking values "helix" or "coil", and solely local interactions. Hence, in such theories thermodynamic phase transitions are not possible. However, in preliminary work [4] it was shown that our all-atom model of poly-alanine exhibits a phase transition between the ordered helical state and the disordered random-coil state. It was conjectured that this transition is due to long range interactions in our model and the fact that it is not one-dimensional: it is known that the 1D Ising model with long-range interactions also exhibits a phase transition at finite T if the interactions decay like 1/r σ with 1 ≤ σ < 2 [6]. Our aim now is to investigate this transition in the frame work of a critical theory by means of the finite size scaling (FSS) analysis of partition function zeros. Analysis of partition function zeros is a well-known tool in the study of phase transitions, but was to our knowledge never used before to study biopolymers.For our project, the use of the multicanonical algorithm [7] was crucial. The various competing interactions within the polymer lead to an energy landscape characterized by a multitude of local minima. Hence, in the low-temperature region, canonical simulations will tend to get trapped in one of these minima and the simulation will not thermalize within the available CPU time. One standard way to overcome this problem is the application of the multicanonical algorithm [7] and other generalized-ensemble techniques [8] to the protein folding problem [9]. For poly-alanine, both the failure of standard Monte Carlo techniques and the superior performance of the multicanonical algorithm are extensively documented in earlier work [10].In the multicanonical algorithm [7] conformations with energy E are assigned a weight w mu (E) ∝ 1/n(E). Here, n(E) is the density of states. A simulation with this weight will lead to a uniform distribution of energy:This is because the simulation generates a 1D random walk in the energy, allowing itself to escape from any local minimum. Since a large range of energies are sampled, one can use the reweighting techniques [11] to calculate thermodynamic quantities over a wide range of...

In this paper we study the short-time behavior of the Blume-Capel model at the tricritical point as well as along the second order critical line. Dynamic and static exponents are estimated by exploring scaling relations for the magnetization and its moments at an early stage of the dynamic evolution. Our estimates for the dynamic exponents, at the tricritical point, are z=2.215(2) and theta=-0.53(2).

The global persistence exponent theta(g) is calculated for the two-dimensional Blume-Capel model following a quench to the critical point from both disordered states and such with small initial magnetizations. Estimates are obtained for the nonequilibrium critical dynamics on the critical line and at the tricritical point. Ising-like universality is observed along the critical line and a different value theta(g)=1.080(4) is found at the tricritical point.

We study helix-coil transitions in an all-atom model of polyalanine. Molecules of up to length 30 residues are investigated by multicanonical simulations. Results from two implicit solvent models are compared with each other and with that from simulations in gas phase. While the helix-coil transition is in all three models a true thermodynamic phase transition, we find that its strength is reduced by the protein-solvent interaction term. The order of the helix-coil transition depends on the details of the solvation term.

No abstract

We have performed Monte Carlo simulations for the three-dimensional Ising model. Using histogram techniques, we calculate the density of states on L block lattices up to size L =14. Statistical jackknife methods are employed to perform a thorough error analysis. We obtain high-precision estimates for the leading zeros of the partition function, which, using finite-size scaling, translate into v=0. 6285+0.0019. Along a different line of approach following recent work in lattice-gauge theories, we accurately determine the mass gap m = I/g (g correlation length) for cylindrical L'L, lattices (with L, =256 and L up to 12). The finite-size-scaling analysis of the mass-gap data leads to v =0.6321%0.0019.

Using new methods to analyze Monte Carlo data, we have calculated the leading partition-function zero for SU(3) lattice gauge theory on various LtL^ lattices. For Li ^4 lattices we find in the range L=*4-16 the scaling behavior of a second-order transition with v=0.468(6). However, for larger lattices (L •=14-24), the scaling behavior is consistent with a first-order transition: v=0.35(2). The firstorder nature of the transition is further substantiated by the fact that the finite-size scaling analysis of the specific heat yields a nonvanishing infinite-volume latent heat.PACS numbers: 1 l.lS.Ha, 12.38.Gc