Random field Ising model: dimensional reduction or spin-glass phase?

The stability of the random field Ising model (RFIM) against spin glass (SG) fluctuations, as investigated by M\'ezard and Young, is naturally expressed via Legendre transforms, stability being then associated with the non-negativeness of eigenvalues of the inverse of a generalized SG susceptibility matrix. It is found that the signal for the occurrence of the SG transition will manifest itself in free-energy {\sl fluctuations\/} only, and not in the free energy itself. Eigenvalues of the inverse SG susceptibility matrix is then approached by the Rayleigh Ritz method which provides an upper bound. Coming from the paramagnetic phase {\sl on the Curie line,\/} one is able to use a virial-like relationship generated by scaling the {\sl single\/} unit length $(D<6;$ in higher dimension a new length sets in, the inverse momentum cut off). Instability towards a SG phase being probed on pairs of {\sl distinct\/} replicas, it follows that, despite the repulsive coupling of the RFIM the effective pair coupling is {\sl attractive\/} (at least for small values of the parameter $g\bar \Delta ,$ $g$ the coupling and $\bar \Delta$ the effective random field fluctuation). As a result, \lq\lq bound states\rq\rq\ associated with replica pairs (negative eigenvalues) provide the instability signature. {\sl Away from the Curie line\/}, the attraction is damped out till the SG transition line is reached and paramagnetism restored. In $D<6,$ the SG transition always precedes the ferromagnetic one, thus the domain in dimension where standard dimensional reduction would apply (on the Curie line) shrinks to zero.Comment: te

A simple model for DNA denaturation

Following Poland and Scheraga, we consider a simplified model for the denaturation transition of DNA. The two strands are modeled as interacting polymer chains. The attractive interactions, which mimic the pairing between the four bases, are reduced to a single short range binding term. Furthermore, base-pair misalignments are forbidden, implying that this binding term exists only for corresponding (same curvilinear abscissae) monomers of the two chains. We take into account the excluded volume repulsion between monomers of the two chains, but neglect intra-chain repulsion. We find that the excluded volume term generates an effective repulsive interaction between the chains, which decays as $1/r^{d-2}$. Due to this long-range repulsion between the chains, the denaturation transition is first order in any dimension, in agreement with previous studies.Comment: 10 page

Ionic profiles close to dielectric discontinuities: Specific ion-surface interactions

We study, by incorporating short-range ion-surface interactions, ionic profiles of electrolyte solutions close to a non-charged interface between two dielectric media. In order to account for important correlation effects close to the interface, the ionic profiles are calculated beyond mean-field theory, using the loop expansion of the free energy. We show how it is possible to overcome the well-known deficiency of the regular loop expansion close to the dielectric jump, and treat the non-linear boundary conditions within the framework of field theory. The ionic profiles are obtained analytically to one-loop order in the free energy, and their dependence on different ion-surface interactions is investigated. The Gibbs adsorption isotherm, as well as the ionic profiles are used to calculate the surface tension, in agreement with the reverse Hofmeister series. Consequently, from the experimentally-measured surface tension, one can extract a single adhesivity parameter, which can be used within our model to quantitatively predict hard to measure ionic profiles.Comment: 14 pages, 6 figure

Anharmonicity and self-similarity of the free energy landscape of protein G

The near-native free energy landscape of protein G is investigated through 0.4 microseconds-long atomistic molecular dynamics simulations in explicit solvent. A theoretical and computational framework is used to assess the time-dependence of salient thermodynamical features. While the quasi-harmonic character of the free energy is found to degrade in a few ns, the slow modes display a very mild dependence on the trajectory duration. This property originates from a striking self-similarity of the free energy landscape embodied by the consistency of the principal directions of the local minima, where the system dwells for several ns, and of the virtual jumps connecting them.Comment: revtex, 6 pages, 5 figure

Coherent States Formulation of Polymer Field Theory

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards' well known auxiliary-field (AF) framework, the CS formulation does not contain an embedded non-linear, non-local functional of the auxiliary fields, and the action of the field theory has a fully explicit, finite-order and semi-local polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.Comment: 14pages 8 figure

Low volumes of quartz cement in deeply buried Fulmar Formation sandstones explained by a low effective stress burial history

Upper Jurassic Fulmar Formation sandstones from the Fulmar Field in the Central North Sea are buried to 3.2 km and 128 °C but contain only 3.7 ± 1.7% (1σ) quartz cement, substantially less than volumes predicted by models based on temperature-related quartz precipitation kinetics. Oxygen isotope microanalysis of quartz overgrowths suggests that only limited cementation occurred at temperatures above 110 °C. We suggest that the anomalously low volumes of quartz cement are most readily explained by the effective stress history of the Fulmar Formation. Regional pore pressure analysis strongly suggests that pore fluid pressures in the Fulmar Formation decreased substantially in the last <0.5 Ma as a result of lateral seal failure, increasing effective stress from ca. 10 MPa to the current 31 MPa. A recent increase in effective stress is supported by the common occurrence of grains that are both fractured and unhealed by quartz cement. Intergranular pressure dissolution can account for around one third of the observed quartz cement, with the remainder from deep burial feldspar dissolution. We argue that the continuous history of low effective stress, until the very recent geological past, limited the rate of silica supply by intergranular pressure dissolution, and thus the rate of quartz cementation. Effective stress histories should be incorporated into predictive models of quartz cementation of sandstones

A meaningful expansion around detailed balance

We consider Markovian dynamics modeling open mesoscopic systems which are driven away from detailed balance by a nonconservative force. A systematic expansion is obtained of the stationary distribution around an equilibrium reference, in orders of the nonequilibrium forcing. The first order around equilibrium has been known since the work of McLennan (1959), and involves the transient irreversible entropy flux. The expansion generalizes the McLennan formula to higher orders, complementing the entropy flux with the dynamical activity. The latter is more kinetic than thermodynamic and is a possible realization of Landauer's insight (1975) that, for nonequilibrium, the relative occupation of states also depends on the noise along possible escape routes. In that way nonlinear response around equilibrium can be meaningfully discussed in terms of two main quantities only, the entropy flux and the dynamical activity. The expansion makes mathematical sense as shown in the simplest cases from exponential ergodicity.Comment: 19 page

The elusive quest for RNA knots

Physical entanglement, and particularly knots arise spontaneously in equilibrated polymers that are sufficiently long and densely packed. Biopolymers are no exceptions: knots have long been known to occur in proteins as well as in encapsidated viral DNA. The rapidly growing number of RNA structures has recently made it possible to investigate the incidence of physical knots in this type of biomolecule, too. Strikingly, no knots have been found to date in the known RNA structures. In this Point of View Article we discuss the absence of knots in currently available RNAs and consider the reasons why knots in RNA have not yet been found, despite the expectation that they should exist in Nature. We conclude by singling out a number of RNA sequences that, based on the properties of their predicted secondary structures, are good candidates for knotted RNAs

Field theoretic approach to the counting problem of Hamiltonian cycles of graphs

A Hamiltonian cycle of a graph is a closed path that visits each site once and only once. I study a field theoretic representation for the number of Hamiltonian cycles for arbitrary graphs. By integrating out quadratic fluctuations around the saddle point, one obtains an estimate for the number which reflects characteristics of graphs well. The accuracy of the estimate is verified by applying it to 2d square lattices with various boundary conditions. This is the first example of extracting meaningful information from the quadratic approximation to the field theory representation.Comment: 5 pages, 3 figures, uses epsf.sty. Estimates for the site entropy and the gamma exponent indicated explicitl