Lattice ϕ4\phi^4 theory of finite-size effects above the upper critical dimension

We present a perturbative calculation of finite-size effects near $T_c$ of the $\phi^4$ lattice model in a $d$-dimensional cubic geometry of size $L$ with periodic boundary conditions for $d > 4$. The structural differences between the $\phi^4$ lattice theory and the $\phi^4$ field theory found previously in the spherical limit are shown to exist also for a finite number of components of the order parameter. The two-variable finite-size scaling functions of the field theory are nonuniversal whereas those of the lattice theory are independent of the nonuniversal model parameters.One-loop results for finite-size scaling functions are derived. Their structure disagrees with the single-variable scaling form of the lowest-mode approximation for any finite $\xi/L$ where $\xi$ is the bulk correlation length. At $T_c$, the large-$L$ behavior becomes lowest-mode like for the lattice model but not for the field-theoretic model. Characteristic temperatures close to $T_c$ of the lattice model, such as $T_{max}(L)$ of the maximum of the susceptibility $\chi$, are found to scale asymptotically as $T_c - T_{max}(L) \sim L^{-d/2}$, in agreement with previous Monte Carlo (MC) data for the five-dimensional Ising model. We also predict $\chi_{max} \sim L^{d/2}$ asymptotically. On a quantitative level, the asymptotic amplitudes of this large -$L$ behavior close to $T_c$ have not been observed in previous MC simulations at $d = 5$ because of nonnegligible finite-size terms $\sim L^{(4-d)/2}$ caused by the inhomogeneous modes. These terms identify the possible origin of a significant discrepancy between the lowest-mode approximation and previous MC data. MC data of larger systems would be desirable for testing the magnitude of the $L^{(4-d)/2}$ and $L^{4-d}$ terms predicted by our theory.Comment: Accepted in Int. J. Mod. Phys.

Field theory of bicritical and tetracritical points. III. Relaxational dynamics including conservation of magnetization (Model C)

We calculate the relaxational dynamical critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry including conservation of magnetization by renormalization group (RG) theory within the minimal subtraction scheme in two loop order. Within the stability region of the Heisenberg fixed point and the biconical fixed point strong dynamical scaling holds with the asymptotic dynamical critical exponent $z=2\phi/\nu-1$ where $\phi$ is the crossover exponent and $\nu$ the exponent of the correlation length. The critical dynamics at $n_\|=1$ and $n_\perp=2$ is governed by a small dynamical transient exponent leading to nonuniversal nonasymptotic dynamical behavior. This may be seen e.g. in the temperature dependence of the magnetic transport coefficients.Comment: 6 figure

Field theory of bi- and tetracritical points: Relaxational dynamics

We calculate the relaxational dynamical critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry by renormalization group method within the minimal subtraction scheme in two loop order. The three different bicritical static universality classes previously found for such systems correspond to three different dynamical universality classes within the static borderlines. The Heisenberg and the biconical fixed point lead to strong dynamic scaling whereas in the region of stability of the decoupled fixed point weak dynamic scaling holds. Due to the neighborhood of the stability border between the strong and the weak scaling dynamic fixed point corresponding to the static biconical and the decoupled fixed point a very small dynamic transient exponent, of $\omega_v^{{\cal B}}=0.0044$, is present in the dynamics for the physically important case $n_\|=1$ and $n_\perp=2$ in $d=3$.Comment: 8 figure

Scaling of thermal conductivity of helium confined in pores

We have studied the thermal conductivity of confined superfluids on a bar-like geometry. We use the planar magnet lattice model on a lattice $H\times H\times L$ with $L \gg H$. We have applied open boundary conditions on the bar sides (the confined directions of length $H$) and periodic along the long direction. We have adopted a hybrid Monte Carlo algorithm to efficiently deal with the critical slowing down and in order to solve the dynamical equations of motion we use a discretization technique which introduces errors only $O((\delta t)^6)$ in the time step $\delta t$. Our results demonstrate the validity of scaling using known values of the critical exponents and we obtained the scaling function of the thermal resistivity. We find that our results for the thermal resistivity scaling function are in very good agreement with the available experimental results for pores using the tempComment: 5 two-column pages, 3 figures, Revtex

Variations in the onset diameter for Martian layered ejecta morphologies and their implications for subsurface volatile reservoirs

We investigated regional variations in the onset diameter of craters displaying a single layer ejecta morphology within +/- 30 degrees latitude using Viking imagery. Our results generally agree with those of previous studies which show onset diameters of 5 to 6 km in the equatorial region, but we have identified localized regions with unusually small onset diameters. The largest region is located in Solis and Thaumasia Planae. The 3-5 km onset diameter range in this area indicates a near-surface ice-rich reservoir (depth similar to 110 m). This unusual concentration of near-surface ice may have resulted from magmatic-driven uplifts associated with the Tharsis rise, which modified parts of a regional aquifer/drainage basin system and resulted in the transfer and concentration of subsurface volatiles in this region

Critical Behavior of O(n)-symmetric Systems With Reversible Mode-coupling Terms: Stability Against Detailed-balance Violation

We investigate nonequilibrium critical properties of $O(n)$-symmetric models with reversible mode-coupling terms. Specifically, a variant of the model of Sasv\'ari, Schwabl, and Sz\'epfalusy is studied, where violation of detailed balance is incorporated by allowing the order parameter and the dynamically coupled conserved quantities to be governed by heat baths of different temperatures $T_S$ and $T_M$, respectively. Dynamic perturbation theory and the field-theoretic renormalization group are applied to one-loop order, and yield two new fixed points in addition to the equilibrium ones. The first one corresponds to $\Theta = T_S / T_M = \infty$ and leads to model A critical behavior for the order parameter and to anomalous noise correlations for the generalized angular momenta; the second one is at $\Theta = 0$ and is characterized by mean-field behavior of the conserved quantities, by a dynamic exponent $z = d / 2$ equal to that of the equilibrium SSS model, and by modified static critical exponents. However, both these new fixed points are unstable, and upon approaching the critical point detailed balance is restored, and the equilibrium static and dynamic critical properties are recovered.Comment: 18 pages, RevTeX, 1 figure included as eps-file; submitted to Phys. Rev.

Five-loop additive renormalization in the phi^4 theory and amplitude functions of the minimally renormalized specific heat in three dimensions

We present an analytic five-loop calculation for the additive renormalization constant A(u,epsilon) and the associated renormalization-group function B(u) of the specific heat of the O(n) symmetric phi^4 theory within the minimal subtraction scheme. We show that this calculation does not require new five-loop integrations but can be performed on the basis of the previous five-loop calculation of the four-point vertex function combined with an appropriate identification of symmetry factors of vacuum diagrams. We also determine the amplitude functions of the specific heat in three dimensions for n=1,2,3 above T_c and for n=1 below T_c up to five-loop order. Accurate results are obtained from Borel resummations of B(u) for n=1,2,3 and of the amplitude functions for n=1. Previous conjectures regarding the smallness of the resummed higher-order contributions are confirmed. Borel resummed universal amplitude ratios A^+/A^- and a_c^+/a_c^- are calculated for n=1.Comment: 30 pages REVTeX, 3 PostScript figures, submitted to Phys. Rev.

Is There a Metabolic Program in the Skeletal Muscle of Obese Individuals?

Severe obesity (BMI ≥ 40 kg/m2) is associated with multiple defects in skeletal muscle which contribute to insulin resistance and a reduction in fatty acid oxidation (FAO) in this tissue. These metabolic derangements are retained in human skeletal muscle cells raised in culture. Together, these findings are indicative of a dysfunctional global metabolic program with severe obesity which is of an epigenetic or genetic origin. Weight loss via gastric bypass surgery can “turn off” and/or correct components of this metabolic program as insulin sensitivity is restored; however, the impairment in FAO in skeletal muscle remains evident. Physical activity can improve FAO and insulin action, indicating that this patient population is not exercise resistant and that exercise offers a pathway to circumvent the abnormal program. Findings presented in this review will hopefully increase the understanding of and aid in preventing and/or treating the severely obese condition