A. Nihat Berker

Inverted Berezinskii-Kosterlitz-Thouless singularity and high-temperature algebraic order in an ising model on a scale-free hierarchical-lattice small-world network

We have obtained exact results for the Ising model on a hierarchical lattice incorporating three key features characterizing many real-world networks--a scale-free degree distribution, a high clustering coefficient, and the small-world effect. By varying the probability p of long-range bonds, the entire spectrum from an unclustered, non-small-world network to a highly clustered, small-world system is studied. Using the self-similar structure of the network, we obtain analytic expressions for the degree distribution P(k) and clustering coefficient C for all p, as well as the average path length l for p = 0 and 1. The ferromagnetic Ising model on this network is studied through an exact renormalization-group transformation of the quenched bond probability distribution, using up to 562,500 renormalized probability bins to represent the distribution. For p < 0.494, we find power-law critical behavior of the magnetization and susceptibility, with critical exponents continuously varying with p, and exponential decay of correlations away from Tc. For p > or = 0.494, in fact where the network exhibits small-world character, the critical behavior radically changes: We find a highly unusual phase transition, namely an inverted Berezinskii-Kosterlitz-Thouless singularity, between a low-temperature phase with nonzero magnetization and finite correlation length and a high-temperature phase with zero magnetization and infinite correlation length, with power-law decay of correlations throughout the phase. Approaching Tc from below, the magnetization and the susceptibility, respectively, exhibit the singularities of exp(-C/square root of Tc - T) and exp(D/square root of Tc - T), with C and D positive constants. With long-range bond strengths decaying with distance, we see a phase transition with power-law critical singularities for all p, and evaluate an unusually narrow critical region and important corrections to power-law behavior that depend on the exponent characterizing the decay of long-range interactions.

Dimensionality effects on the multicritical phase diagrams of the Blume–Emery–Griffiths model with repulsive biquadratic coupling: Mean‐field and renormalization‐group studies

Six new phase diagrams, including a novel multicritical topology and two new ordered phases, are obtained by the global mean‐field theory of the spin‐1 Ising model with only nearest‐neighbor interactions, for negative biquadratic couplings. Renormalization‐group studies indicate a threshold spatial dimension, above and below which different sequences of phase diagrams occur.

Critical behavior induced by quenched disorder

Domain arguments and renormalization-group calculations indicate that all temperature-driven symmetry-breaking first-order phase transitions are converted to second order by quenched bond randomness. This occurs for infinitesimal randomness in d⩽2 or d⩽4 respectively for discrete or continuous (n = 1 or n⩾2 component) microscopic degrees of freedom. Even strongly first-order transitions undergo this conversion to second order! Above these dimensions this conversion still occurs but requires a threshold bond randomness, presumably with an intervening new tricritical point. For example, q-state Potts transitions can be made second order for any q in any d, via bond randomness. Non-symmetry-breaking “temperature-driven” first-order transitions are eliminated under the above conditions. These quenched-fluctuation-induced second-order phase transitions suggest the possibility of new universality classes of criticality and tricriticality.

Theory and simulations of water flow through carbon nanotubes: prospects and pitfalls

We study water flow through carbon nanotubes using continuum theory and molecular dynamics simulations. The large slip length in carbon nanotubes greatly enhances the pumping and electrokinetic energy conversion efficiency. In the absence of mobile charges, however, the electro-osmotic flow vanishes. Uncharged nanotubes filled with pure water can therefore not be used as electric field-driven pumps, contrary to some recently ventured ideas. This is in agreement with results from a generalized hydrodynamic theory that includes the angular momentum of rotating dipolar molecules. The electro-osmotic flow observed in simulations of such carbon nanotubes is caused by an imprudent implementation of the Lennard-Jones cutoff. We also discuss the influence of other simulation parameters on the spurious electro-osmotic flow.

Strong violation of critical phenomena universality : Wang-Landau study of the two-dimensional Blume-Capel model under bond randomness

We study the pure and random-bond versions of the square lattice ferromagnetic Blume-Capel model, in both the first-order and second-order phase transition regimes of the pure model. Phase transition temperatures, thermal and magnetic critical exponents are determined for lattice sizes in the range L=20-100 via a sophisticated two-stage numerical strategy of entropic sampling in dominant energy subspaces, using mainly the Wang-Landau algorithm. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the two-dimensional Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections, our findings thus supporting the marginal irrelevance of quenched bond randomness. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with nu=1.30(6) and beta/nu = 0.128(5) . These results amount to a strong violation of universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two sets of results supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional systems with and without quenched disorder. In the conversion by bond randomness of the first-order transition of the pure system to second order, we detect, by introducing and evaluating connectivity spin densities, a microsegregation that also explains the increase we find in the phase transition temperature under bond randomness.

Multicritical Points and Crossover Mediating the Strong Violation of Universality: Wang-Landau Determinations in the Random-Bond d = 2 Blume-Capel model

The effects of bond randomness on the phase diagram and critical behavior of the square lattice ferromagnetic Blume-Capel model are discussed. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method for many values of the crystal field, restricted here in the second-order phase-transition regime of the pure model. For the random-bond version several disorder strengths are considered. We present phase diagram points of both pure and random versions and for a particular disorder strength we locate the emergence of the enhancement of ferromagnetic order observed in an earlier study in the ex-first-order regime. The critical properties of the pure model are contrasted and compared to those of the random model. Accepting, for the weak random version, the assumption of the double-logarithmic scenario for the specific heat we attempt to estimate the range of universality between the pure and random-bond models. The behavior of the strong disorder regime is also discussed and a rather complex and yet not fully understood behavior is observed. It is pointed out that this complexity is related to the ground-state structure of the random-bond version.

Absence of temperature‐driven first‐order phase transitions in systems with random bonds (invited)

Temperature‐driven first‐order phase transitions that involve symmetry breaking are converted to second order by the introduction of infinitesimal quenched bond randomness in spatial dimensions d≤2 or d≤4, respectively, for systems of n=1 or n≥ (R18)2 component microscopic degrees of freedom. Even strongly first‐order transitions undergo this conversion to second order! Above these dimensions, this phenomenon still occurs, but requires a threshold amount of bond randomness. For example, under bond randomness, the phase transitions of q‐state Potts models are second order for all q in d≤2. If no symmetry breaking is involved, temperature‐driven first‐order phase transitions are eliminated under the above conditions. Another consequence is that bond randomness drastically alters multicritical phase diagrams. Tricritical points and critical endpoints are entirely eliminated (d≤2) or depressed in temperature (d≳2). Similarly, bicritical phase diagrams are converted (d≤2) to reentrant‐disorder‐line or decouple...

Molecular tail lengths, dipole pairings, and multiple reentrance mechanisms of liquid crystals

Employing the “spin-gas” model which incorporates the inherent microscopic frustration of dipoles, observed sequences of reentrant nematic and smectic phases are reproduced. In particular, the quadruple reentrance (nematic ↔ smecticAd ↔ nematic ↔ smecticAd ↔ nematic ↔ smecticA1) is explained. The molecular tail length theoretically required for this phenomenon agrees with experiment. In the theory, associations if correlated triplets of molecules propagate smectic order. By contrast, dipole pairings giving rise to dimers of molecules frustrate smectic order and favor the nematic phase. Calculated dimer concentrations are insensitive to N ↔ Ad transitions, consistently with dielectric measurements, whereas dimers break up at the N ↔ A1 transition, causing the large transition enthalpy.

Chaotic spin glasses: An upper critical dimension (invited)

The chaotic renormalization‐group trajectories exhibited by frustrated hierarchical Ising models have been interpreted as signaling a spin‐glass phase, since, as the system is probed at successive length scales, strong and weak correlations are encountered in a chaotic sequence. Cluster‐hierarchical models have been introduced, with susceptibilities behaving as in Bravais lattices. Frustrated cluster‐hierarchical models again show an ordered phase characterized by chaotic rescaling and a smooth specific heat at the transition (α<−5). Scans in dimensionality reveal an upper critical dimension for the chaotic spin‐glass phase, via a boundary crisis mechanism. Beyond this dimension, the system has no long‐range order at any temperature. Nevertheless, a low‐temperature regime can be distinctly identified, exhibiting intermediate‐range chaotic spin‐glass order.

Amorphously packed, frustrated hierarchical models: Chaotic rescaling and spin‐glass behavior

Hierarchical Ising models have been constructed with competing ferromagnetic and antiferromagnetic interactions, and solved exactly. As frustration is increased, a low‐temperature phase is encountered, characterized by chaotic renormalization‐group trajectories. This spin‐glass phase is microscopically described in terms of subsets of spins which are strongly correlated, yet noncontiguous. Further, the amorphous packing of real systems is approximated in these models by a random distribution of shapes at various hierarchical levels, which eliminates unphysical limit cycle behavior in favor of chaos.