Statistical mechanics of the random K-SAT model

The Random K-Satisfiability Problem, consisting in verifying the existence of an assignment of N Boolean variables that satisfy a set of M=alpha N random logical clauses containing K variables each, is studied using the replica symmetric framework of diluted disordered systems. We present an exact iterative scheme for the replica symmetric functional order parameter together for the different cases of interest K=2, K>= 3 and K>>1. The calculation of the number of solutions, which allowed us [Phys. Rev. Lett. 76, 3881 (1996)] to predict a first order jump at the threshold where the Boolean expressions become unsatisfiable with probability one, is thoroughly displayed. In the case K=2, the (rigorously known) critical value (alpha=1) of the number of clauses per Boolean variable is recovered while for K>=3 we show that the system exhibits a replica symmetry breaking transition. The annealed approximation is proven to be exact for large K.Comment: 34 pages + 1 table + 8 fig., submitted to Phys. Rev. E, new section added and references update

Absence of an equilibrium ferromagnetic spin glass phase in three dimensions

Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3-d spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up till the critical value where ferromagnetic ordering sets in, and no ferromagnetic spin glass phase. This phase diagram is in conflict with the droplet/scaling and mean field theories of spin glasses. We also find that the exponents of the second order ferromagnetic transition do not depend on the microscopic Hamiltonian, suggesting universality of this transition.Comment: 4 pages, 5 figures, revte

From simple to complex networks: inherent structures, barriers and valleys in the context of spin glasses

Given discrete degrees of freedom (spins) on a graph interacting via an energy function, what can be said about the energy local minima and associated inherent structures? Using the lid algorithm in the context of a spin glass energy function, we investigate the properties of the energy landscape for a variety of graph topologies. First, we find that the multiplicity Ns of the inherent structures generically has a lognormal distribution. In addition, the large volume limit of ln/ differs from unity, except for the Sherrington-Kirkpatrick model. Second, we find simple scaling laws for the growth of the height of the energy barrier between the two degenerate ground states and the size of the associated valleys. For finite connectivity models, changing the topology of the underlying graph does not modify qualitatively the energy landscape, but at the quantitative level the models can differ substantially.Comment: 10 pages, 9 figs, slightly improved presentation, more references, accepted for publication in Phys Rev

Mean field and corrections for the Euclidean Minimum Matching problem

Consider the length $L_{MM}^E$ of the minimum matching of N points in d-dimensional Euclidean space. Using numerical simulations and the finite size scaling law $= \beta_{MM}^E(d) N^{1-1/d}(1+A/N+... )$, we obtain precise estimates of $\beta_{MM}^E(d)$ for $2 \le d \le 10$. We then consider the approximation where distance correlations are neglected. This model is solvable and gives at $d \ge 2$ an excellent ``random link'' approximation to $\beta_{MM}^E(d)$. Incorporation of three-link correlations further improves the accuracy, leading to a relative error of 0.4% at d=2 and 3. Finally, the large d behavior of this expansion in link correlations is discussed.Comment: source and one figure. Submitted to PR

HTL Resummation of the Thermodynamic Potential

Starting from the Phi-derivable approximation scheme at leading-loop order, the thermodynamical potential in a hot scalar theory, as well as in QED and QCD, is expressed in terms of hard thermal loop propagators. This nonperturbative approach is consistent with the leading-order perturbative results, ultraviolet finite, and, for gauge theories, explicitly gauge-invariant. For hot QCD it is argued that the resummed approximation is applicable in the large-coupling regime, down to almost twice the transition temperature.Comment: minor changes, to appear in PRD, 27 pages, 15 eps figure

Efecto del tratamiento J-Synch sobre el porcentaje de preñez en vaquillonas para cría inseminadas a tiempo fijo

The objective of the present work was to evaluate the effect of J-Synch protocol used in heifers on pregnancy rate submitted to fixed time artificial insemination (FTAI). Six hundred and thirteen Angus heifers were used (age range: 13.5 to 15 months; body condition: 3 to 3.5 -scale 1 to 5 (1: emaciated and 5: obese) and weight: ≥ 260 kg. The animals were randomly assigned to the experimental units (heifers) according to a completely randomized design, to the following group: 1) J-Synch (n=205): on day 0 an intravaginal device was inserted with 0.6 g of progesterone (IVD) plus 2 mg of estradiol benzoate. On day 6 the device was removal and 0.15 mg of d-cloprostenol was administered. On day 9 (70-72 h after device removal), 0.10 mg of buserelin was injected and FTAI was performed. 2) Conventional 7D (n=206): on day 0 an intravaginal device (IVD) was inserted plus 2 mg of estradiol benzoate. On day 7 the device was removed and 0.15 mg of d-cloprostenol and 0.5 mg of estradiol cypionate were administered. On day 9 (50-52 h after device removal), FTAI was performed. 3) Conventional 8D (n=202): similar to Conventional group 7D, with the exception that the device remained in the vagina for a period of 8 days. For FTAI, frozen / thawed semen from a bull of proven fertility was used. Gestation diagnosis were performed at 30 days after FTAI. The statistical analysis was made by SAS. A 95% confidence level was established (α=0.05). Animals that lost the device (3.4%) were excluded from the statistical analysis. The pregnancy rate was not different between treatments (J-synch: 50.8%, Conventional 7D: 43.4% and Conventional 8D: 47.7%, p>0.05). In conclusion, J-Synch treatment used in beef heifers (13.5-15 months of age) generates pregnancy rate after FTAI similar to conventional treatment.El objetivo del trabajo fue evaluar el efecto del J-Synch en vaquillonas para cría sobre el porcentaje de preñez post inseminación artificial a tiempo fijo (IATF). Se utilizaron 613 vaquillonas Angus (edad: 13,5 a 15 meses; condición corporal: 3 a 3,5 - escala 1 a 5 (1: emaciada, 5: obesa) y peso: ≥ 260 kg). Los animales fueron asignados aleatoriamente a 3 grupos de unidades experimentales (diseño completamente aleatorizado): 1) J-Synch (n=205): el día 0 se colocó un dispositivo intravaginal con 0,6 g de progesterona (DISP) más 2 mg de benzoato de estradiol (BE). El día 6 se retiró el DISP y se administró 0,15 mg de d-cloprostenol. El día 9 (70-72 h post retiro del DISP), se inyectó 0,10 mg de buserelina y se realizó IATF. 2) Convencional 7D (n=206): el día 0 se colocó un DISP más 2 mg de BE. El día 7 se retiró el DISP y se administraron 0,15 mg de d-cloprostenol y 0,5 mg de cipionato de estradiol. El día 9 (50-52 h post DISP) se realizó IATF. 3) Convencional 8D (n=202): ídem grupo Convencional 7D, con la salvedad que el DISP permaneció colocado durante 8 días. Para la IATF se utilizó semen congelado/descongelado proveniente de un toro de probada fertilidad. El diagnóstico de gestación se realizó a los 30 días post IATF. El análisis estadístico se realizó por SAS (nivel de confianza: 95%). Los animales que perdieron el dispositivo fueron excluidos del análisis. El 3,4% de las vaquillonas perdieron el DISP. El porcentaje de preñez no difirió entre tratamientos (J-Synch: 50,8%; Convencional 7D: 43,4% y Convencional 8D: 47,7%, p>0,05). Se concluye que el tratamiento J-Synch utilizado en vaquillonas para cría (13,5-15 meses de edad) genera porcentajes de preñez post IATF similares al tratamiento convencional

Random Resistor-Diode Networks and the Crossover from Isotropic to Directed Percolation

By employing the methods of renormalized field theory we show that the percolation behavior of random resistor-diode networks near the multicritical line belongs to the universality class of isotropic percolation. We construct a mesoscopic model from the general epidemic process by including a relevant isotropy-breaking perturbation. We present a two-loop calculation of the crossover exponent $\phi$. Upon blending the $\epsilon$-expansion result with the exact value $\phi =1$ for one dimension by a rational approximation, we obtain for two dimensions $\phi = 1.29\pm 0.05$. This value is in agreement with the recent simulations of a two-dimensional random diode network by Inui, Kakuno, Tretyakov, Komatsu, and Kameoka, who found an order parameter exponent $\beta$ different from those of isotropic and directed percolation. Furthermore, we reconsider the theory of the full crossover from isotropic to directed percolation by Frey, T\"{a}uber, and Schwabl and clear up some minor shortcomings.Comment: 24 pages, 2 figure

Multifractal properties of resistor diode percolation

Focusing on multifractal properties we investigate electric transport on random resistor diode networks at the phase transition between the non-percolating and the directed percolating phase. Building on first principles such as symmetries and relevance we derive a field theoretic Hamiltonian. Based on this Hamiltonian we determine the multifractal moments of the current distribution that are governed by a family of critical exponents $\{\psi_l \}$. We calculate the family $\{\psi_l \}$ to two-loop order in a diagrammatic perturbation calculation augmented by renormalization group methods.Comment: 21 pages, 5 figures, to appear in Phys. Rev.

Efecto de dos dosis de cipionato de estradiol y del rango horario para la IATF sobre la tasa de preñez en vaquillonas

El objetivo de este trabajo fue evaluar el efecto de dos dosis de cipionato de estradiol (CPE) y dos intervalos para realizar la inseminación, sobre el porcentaje de preñez a la inseminación artificial a tiempo fijo (IATF). Se utilizaron 326 vaquillonas de 24 meses, Angus negro (AAN) y colorado (AAC), de condición corporal (media±de) 3,7±0,3 (escala 1-5). El día 0 se les colocó un dispositivo intravaginal con proges­terona (DISP, DIB 0,5, Syntex) más 2 mg de benzoato de estradiol (Estradiol 10, Río de Ja­neiro) im. El día 8 se retiró el DISP, se administró im 150 mg de D(+) Cloprostenol (Arsaprost, ARSA) y los animales recibieron aleatoriamente 0,5 o 1 mg de cipionato de estradiol (Grupo CPE05 y CPE1, respectivamente). El día 10 las vaquillonas fueron inseminadas, dentro de cada tratamiento, a las 48-52 h o 53-58 h post-retiro de los dispositivos. Se utilizó semen de dos toros (A y B), los cuales estuvieron distribuidos aleatoriamente dentro de cada raza, tra­tamiento y rango horario. El diagnóstico de gestación se realizó por palpación transrrectal a los 63 días de realizada la IATF. Se evaluó el efecto raza (AAN y AAC), tratamiento (CPE05 o CPE1), toro (A y B), hora de IATF (48-52 y 53-58) y las interacciones dobles sobre el por­centaje de preñez. Se utilizó el PROC CATMOD del SAS, fijando un nivel de confianza del 95% (α=0,05). No se observaron efectos significativos de la raza (AAC: 49,1%; AAN: 57,1%), tratamiento (CPE05: 51,6%; CPE1: 51,5%), toro (A: 54,6%, B: 48,5%), hora de IATF (48-52: 54,4%; 53-58: 48,8%) o sus interacciones dobles (p>0,05)

Field theory of directed percolation with long-range spreading

It is well established that the phase transition between survival and extinction in spreading models with short-range interactions is generically associated with the directed percolation (DP) universality class. In many realistic spreading processes, however, interactions are long ranged and well described by L\'{e}vy-flights, i.e., by a probability distribution that decays in $d$ dimensions with distance $r$ as $r^{-d-\sigma}$. We employ the powerful methods of renormalized field theory to study DP with such long range, L\'{e}vy-flight spreading in some depth. Our results unambiguously corroborate earlier findings that there are four renormalization group fixed points corresponding to, respectively, short-range Gaussian, L\'{e}vy Gaussian, short-range DP and L\'{e}vy DP, and that there are four lines in the $(\sigma, d)$ plane which separate the stability regions of these fixed points. When the stability line between short-range DP and L\'{e}vy DP is crossed, all critical exponents change continuously. We calculate the exponents describing L\'{e}vy DP to second order in $\epsilon$-expansion, and we compare our analytical results to the results of existing numerical simulations. Furthermore, we calculate the leading logarithmic corrections for several dynamical observables.Comment: 12 pages, 3 figure