Minimal renormalization without \epsilon-expansion: Three-loop amplitude functions of the O(n) symmetric \phi^4 model in three dimensions below T_c

We present an analytic three-loop calculation for thermodynamic quantities of the O(n) symmetric \phi^4 theory below T_c within the minimal subtraction scheme at fixed dimension d=3. Goldstone singularities arising at an intermediate stage in the calculation of O(n) symmetric quantities cancel among themselves leaving a finite result in the limit of zero external field. From the free energy we calculate the three-loop terms of the amplitude functions f_phi, F+ and F- of the order parameter and the specific heat above and below T_c, respectively, without using the \epsilon=4-d expansion. A Borel resummation for the case n=2 yields resummed amplitude functions f_phi and F- that are slightly larger than the one-loop results. Accurate knowledge of these functions is needed for testing the renormalization-group prediction of critical-point universality along the \lambda-line of superfluid He(4). Combining the three-loop result for F- with a recent five-loop calculation of the additive renormalization constant of the specific heat yields excellent agreement between the calculated and measured universal amplitude ratio A+/A- of the specific heat of He(4). In addition we use our result for f_phi to calculate the universal combination R_C of the amplitudes of the order parameter, the susceptibility and the specific heat for n=2 and n=3. Our Borel-resummed three-loop result for R_C is significantly more accurate than the previous result obtained from the \epsilon-expansion up to O(\epsilon^2).Comment: 29 pages LaTeX including 3 PostScript figures, to appear in Nucl. Phys. B [FS] (1998

Tectonic setting of Martian volcanoes and deep-seated intrusives

More than 50 volcanoes have been mapped on Mars, and recent geologic studies indicate structural evidence of deep seated intrusive bodies. Most volcanoes in the Tharsis region are volcanotectonic features; they have been associated with large scale tectonic and volcanic processes. They occur along complex systems of faults and grabens having a dominant northwest to southwest trend closely coincident with a great circle, which extends along 90 deg of arc from Tempe Patera to probable volcanic mountains near lat. 40 deg S, long. 150 deg. Deep seated intrusive bodies are also concentrated in the Tharsis region and are recognized mostly where faults have been deflected around their cores. The Elysium Mons-Amphitrites Patera volcanic alignment is subparallel to that of Tharsis but is longer, extending through about 120 deg of arc; it transects the dichotomy boundary and is radial to the Hellas basin. Volcanoes in the Tharsis region have the widest age range of all volcanoes on Mars, as determined by the size-frequency distribution of their craters having diameters of 2, 5, and 16 km

Critical free energy and Casimir forces in rectangular geometries

We study the critical behavior of the free energy and the thermodynamic Casimir force in a $L_\parallel^{d-1} \times L$ block geometry in $2<d<4$ dimensions with aspect ratio $\rho=L/L_\parallel$ above, at, and below $T_c$ on the basis of the O$(n)$ symmetric $\phi^4$ lattice model with periodic boundary conditions (b.c.). We consider a simple-cubic lattice with isotropic short-range interactions. Exact results are derived in the large - $n$ limit describing the geometric crossover from film ($\rho =0$) over cubic $\rho=1$ to cylindrical ($\rho = \infty$) geometries. For $n=1$, three perturbation approaches are presented that cover both the central finite-size regime near $T_c$ for $1/4 \lesssim \rho \lesssim 3$ and the region outside the central finite-size regime well above and below $T_c$ for arbitrary $\rho$. At bulk $T_c$ of isotropic systems with periodic b.c., we predict the critical Casimir force in the vertical $(L)$ direction to be negative (attractive) for a slab ($\rho 1$), and zero for a cube $(\rho=1)$. We also present extrapolations to the cylinder limit ($\rho=\infty$) and to the film limit ($\rho=0$) for $n=1$ and $d=3$. Our analytic results for finite-size scaling functions in the minimal renormalization scheme at fixed dimension $d=3$ agree well with Monte Carlo data for the three-dimensional Ising model by Hasenbusch for $\rho=1$ and by Vasilyev et al. for $\rho=1/6$ above, at, and below $T_c$.Comment: 23 pages, 14 figure

Paleolakes and lacustrine basins on Mars

The problems of how warm and wet Mars once was and when climate transitions may have occurred are not well understood. Mars may have had an early environment similar to Earth's that was conducive to the emergence of life. In addition, increasing geologic evidence indicates that water, upon which terrestrial life depends, has been present on Mars throughout its history. This evidence does not detract from the possibility that life may have originated on early Mars, but rather suggests that life could have developed over longer periods of time in longer lasting, more clement local environments than previously envisioned. It is suggested herein that such environments may have been provided by paleolakes, located mostly in the northern lowlands and probably ice covered. Such lakes probably would have had diverse origins. Glacial lakes may have occupied ice eroded hollows or formed in valleys obstructed by moraines or ice barriers. Unlike Earth, the Martian record of the origin and evolution of possible life may have not been erased by extensive deformation of the surface. Thus the basins that may have contained the paleolakes are potential sites for future biological, geological, and climatological study

Nonuniversal finite-size scaling in anisotropic systems

We study the bulk and finite-size critical behavior of the O$(n)$ symmetric $\phi^4$ theory with spatially anisotropic interactions of non-cubic symmetry in $d<4$ dimensions. In such systems of a given $(d,n)$ universality class, two-scale factor universality is absent in bulk correlation functions, and finite-size scaling functions including the Privman-Fisher scaling form of the free energy, the Binder cumulant ratio and the Casimir amplitude are shown to be nonuniversal. In particular it is shown that, for anisotropic confined systems, isotropy cannot be restored by an anisotropic scale transformation.Comment: 8 pages, 1 figure, accepted for publication in Phys. Rev. E and modifications of tex

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

New Geologic Map of the Argyre Region of Mars: Deciphering the Geologic History Through Mars Global Surveyor, Mars Odyssey, and Mars Express Data

The primary objective of the mapping effort is to produce a geologic map of the Argyre basin and surrounding region at 1:5,000,000 scale in both digital and print formats that will detail the stratigraphic and crosscutting relations among rock materials and landforms (30 deg. S to 65 deg. S, 290 deg. E to 340 deg E). There has not been a detailed geologic map produced of the Argyre region since the Viking-era mapping investigation. The mapping tasks include stratigraphic mapping, crater counting, feature mapping, quantitative landform analysis, and spectroscopic/ stratigraphic investigation feature mapping. The regional geologic mapping investigation includes the Argyre basin floor and rim materials, the transition zone that straddles the Thaumasia plateau, which includes Argyre impactrelated modification, and the southeast margin of the Thaumasia plateau using important new data sets from the Mars Global Surveyor, Mars Odyssey, Mars Express, and Mars Reconnaissance Orbiter. The geologic information unfolded by this new mapping project will be useful to the community for constraining the regional geology, paleohydrology, and paleoclimate, which includes but is not limited to the assessment of: (1) whether the Argyre basin contained lakes, (2) the extent of reported flooding and glaciation, (3) existing interpretations of the origin of the narrow ridges located in the southeast part of the basin floor, and (4) the extent of Argyre-related tectonism and its influence on the surrounding regions