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Nature uses phase transitions as powerful regulators of processes ranging from climate to the alteration of phase behavior of cell membranes to protect cells from cold, building on the fact that thermodynamic properties of a solid, liquid, or gas are sensitive fingerprints of intermolecular interactions. The only known exceptions from this sensitivity are critical points. At a critical point, two phases become indistinguishable and thermodynamic properties exhibit universal behavior: systems with widely different intermolecular interactions behave identically. Here we report a major counterexample. We show that different members of a family of two-dimensional systems —the discrete p-state clock model— with different Hamiltonians describing different microscopic interactions between molecules or spins, may exhibit identical thermodynamic behavior over a wide range of temperatures. The results generate a comprehensive map of the phase diagram of the model and, by virtue of the discrete rotors behaving like continuous rotors, an emergent symmetry, not present in the Hamiltonian. This symmetry, or many-to-one map of intermolecular interactions onto thermodynamic states, demonstrates previously unknown limits for macroscopic distinguishability of different microscopic interactions.

An overview is given of the development of advanced nanoporous carbons as storage ma-terials for natural gas (methane) and molecular hydrogen in on-board fuel tanks for next-generation clean automobiles. The carbons are produced in a multi-step process from corncob, have surface areas of up to 3500 m2/g, porosities of up to 0.8, and reversibly store, by physisorp-tion, record amounts of methane and hydrogen. Current best gravimetric and volumetric storage capacities are: 250 g CH4/kg carbon and 130 g CH4/liter carbon (199 V/V) at 35 bar and 293 K; and 80 g H2/kg carbon and 47 g H2/liter carbon at 47 bar and 77 K. This is the first time the DOE methane storage target of 180 V/V at 35 bar and ambient temperature has been reached and exceeded. The hydrogen values compare favorably with the 2010 DOE gravimetric and volu-metric targets for hydrogen. A prototype adsorbed natural gas (ANG) tank, loaded with carbon monoliths produced accordingly and currently undergoing a road test in Kansas City, is de-scribed. A preliminary analysis of the surface and pore structure is given that may shed light on the mechanisms leading to the extraordinary storage capacities of these materials. The analysis includes pore-size distributions from nitrogen adsorption isotherms; spatial organization of pores across the entire solid from small-angle x-ray scattering (SAXS); pore entrances from scanning electron microscopy (SEM) and transmission electron microscopy (TEM); H2 binding energies from temperature-programmed desorption (TPD); and analysis of surface defects from Raman spectra. For future materials, expected to have higher H2 binding energies via appropriate sur-face functionalization, preliminary projections of H2 storage capacities based on molecular dy-namics simulations of adsorption of H2 on graphite, are reported.

The p-state clock model in two dimensions is a system of discrete rotors with a quasi-liquid phase in a region T1 < T < T2 for p > 4. We show that, for p > 4 and above a temperature Teu, all macroscopic thermal averages, such as energy or magnetization, become identical to those of the continuous rotor (p = \infty). This collapse of thermodynamic observables creates a regime of extended universality in the phase diagram and an emergent symmetry, not present in the Hamiltonian. For p \ge 8, the collapse starts in the quasi-liquid phase and makes the transition at T2 identical to the Berezinskii-Kosterlitz-Thouless (BKT) transition of the con-tinuous rotor. For p \le 6, the transition at T2 is below Teu and no longer BKT. The results generate a comprehensive map of the critical properties at T1 and T2, and a range of experimental predictions, such as motion of magnetic domain walls, fab-rication of identical devices from different building blocks, and limits on macro-scopic distinguishability of different microscopic interactions., 1 PDF file, 4 pages, accepted for publication in Phys. Rev. Lett

A variety of recent experiments probing the low-temperature transport properties of quantum Hall systems have suggested an interpretation in terms of liquid crystalline mesophases dubbed {\em quantum Hall liquid crystals}. The single mode approximation (SMA) has been a useful tool for the determination of the excitation spectra of various systems such as phonons in $^4$He and in the fractional quantum Hall effect. In this paper we calculate (via the SMA) the spectrum of collective excitations in a quantum Hall liquid crystal by considering {\em nematic}, {\em tetratic}, and {\em hexatic} generalizations of Laughlin's trial wave function having two-, four- and six-fold broken rotational symmetry, respectively. In the limit of zero wavevector $\qq$ the dispersion of these modes is singular, with a gap that is dependent on the direction along which $\qq=0$ is approached for {\em nematic} and {\em tetratic} liquid crystalline states, but remains regular in the {\em hexatic} state, as permitted by the fourth order wavevector dependence of the (projected) oscillator strength and static structure factor., Comment: 6 pages, 5 eps figures included

The single mode approximation (SMA) has been a useful tool for the determination of the collective excitation spectra of various systems. For example, Feynman used it successfully for the calculation of the spectrum of sound waves in superfluid 4He [1]; and Girvin, MacDonald and Platzman employed a projected SMA to determine that of the fractional quantum Hall (QH) effect [2] for Laughlin‐like states [3]. In this paper we calculate the excitation spectrum for density fluctuations in a QH liquid crystal. We consider nematic, tetratic, and hexatic generalizations of Laughlin’s trial wave function [3] having two‐, four‐ and six‐fold broken rotational symmetry (BRS) respectively. We perform extensive Monte Carlo (MC) simulations to compute the density‐coupled spectrum of these liquid crystalline states in the lowest Landau levels. We find significant angular dependence of the spectrum with singular behavior for long wavelengths and considerable deepening of the magnetoroton as the anisotropy is increased.

Based on the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory of two-dimensional melting and the analogy between Laughlin states and the two-dimensional one-component plasma (2DOCP), we investigate the possibility of liquid crystalline states in a single Landau level (LL). We introduce many-body trial wavefunctions that are translationally invariant but posess 2-fold (i.e. {\em nematic}), 4-fold ({\em tetratic}) or 6-fold ({\em hexatic}) broken rotational symmetry at respective filling factors $\nu = 1/3$, 1/5 and 1/7 of the valence LL. We find that the above liquid crystalline states exhibit a soft charge density wave (CDW) which underlies the translationally invariant state but which is destroyed by quantum fluctuations. By means of Monte Carlo (MC) simulations, we determine that, for a considerable variety of interaction potentials, the anisotropic states are energetically unfavorable for the lowest and first excited LL's (with index $L = 0, 1$), whereas the nematic is favorable at the second excited LL ($L = 2$)., Comment: 7 figures, submitted to PRB, high-quality figures available upon request

Periodic boundary conditions have not a unique implementation in magnetic systems where all spins interact with each other through a power law decaying interaction of the form $1/r^\alpha$, $r$ being the distance between spins. In this work we present a comparative study of the finite size effects oberved in numerical simulations by using first image convention and full infinite of periodic boundary conditions in one and two-dimensional spin systems with those type of interactions, including the ferromagnetic, antiferromagnetic and competitive interactions cases. Our results show no significative differences between the finite size effects produced by both types of boundary conditions when the low temperature phase has zero global magnetization, while it depends on the ratio $\alpha/d$ for systems with a low temperature ferromagnetic phase. In the last case the first image convention gives much more stronger finite size effects than the other when the system enters into the classical regime $\alpha/d \leq 3/2$., Comment: 9 pages, 5 figures

Nature uses phase transitions as powerful regulators of processes ranging from climate to the alteration of phase behavior of cell membranes, building on the fact that thermodynamic properties of a solid, liquid, or gas are sensitive fingerprints of intermolecular interactions. The only known exceptions from this sensitivity are critical points, where two phases become indistinguishable and thermodynamic properties exhibit universal behavior: systems with widely different intermolecular interactions behave identically. Here we report a new, stronger form of universality, in which different members of a family of two-dimensional systems—the discrete p-state clock model—behave identically both near and away from critical points, if the temperature exceeds a value Teu ('extended universality). We show that all thermal averages are identical to those of the continuous planar rotor model (p = ∞) above Teu, that phase transitions above Teu are identical to the Berezinskii-Kosterlita-Thouless (BKT) transition, and that transitions below Teu are distinctly non-BKT. The results generate a comprehensive map of the three phases of the model and, by virtue of the discrete rotors behaving like continuous rotors, an emergent symmetry, not present in the Hamiltonian. This symmetry, or many-to-one map of intermolecular interactions onto thermodynamic states, demonstrates previously unknown limits for macroscopic distinguishability of different microscopic interactions.