arXiv subjects

A. Nihat Berker

Publications and source records attributed to A. Nihat Berker.

64 records · Page 4Linked to original sources

arXiv2008

Excitation Spectrum Gap and Spin-Wave Stiffness of XXZ Heisenberg Chains: Global Renormalization-Group Calculation

The anisotropic XXZ spin-1/2 Heisenberg chain is studied using renormalization-group theory. The specific heats and nearest-neighbor spin-spin correlations are calculated thoughout the entire temperature and anisotropy ranges in both ferromagnetic and antiferromagnetic regions, obtaining a global description and quantitative results. We obtain, for all anisotropies, the antiferromagnetic spin-liquid spin-wave velocity and the Isinglike ferromagnetic excitation spectrum gap, exhibiting the spin-wave to spinon crossover. A number of characteristics of purely quantum nature are found: The in-plane interaction s_i^x s_j^x + s_i^y s_j^y induces an antiferromagnetic correlation in the out-of-plane s_i^z component, at higher temperatures in the antiferromagnetic XXZ chain, dominantly at low temperatures in the ferromagnetic XXZ chain, and, in-between, at all temperatures in the XY chain. We find that the converse effect also occurs in the antiferromagnetic XXZ chain: an antiferromagnetic s_i^z s_j^z interaction induces a correlation in the s_i^xy component. As another purely quantum effect, (i) in the antiferromagnet, the value of the specific heat peak is insensitive to anisotropy and the temperature of the specific heat peak decreases from the isotropic (Heisenberg) with introduction of either type (Ising or XY) anisotropy; (ii) in complete contrast, in the ferromagnet, the value and temperature of the specific heat peak increase with either type of anisotropy.

cond-mat.stat-mech↗

arXiv2008

Quantum-Mechanically Induced Asymmetry in the Phase Diagrams of Spin-Glass Systems

The spin-1/2 quantum Heisenberg model is studied in all spatial dimensions d by renormalization-group theory. Strongly asymmetric phase diagrams in temperature and antiferromagnetic bond probability p are obtained in dimensions d \geq 3. The asymmetry at high temperatures approaching the pure ferromagnetic and antiferromagnetic systems disappears as d is increased. However, the asymmetry at low but finite temperatures remains in all dimensions, with the antiferromagnetic phase receding to the ferromagnetic phase. A finite-temperature second-order phase boundary directly between the ferromagnetic and antiferromagnetic phases occurs in d \geq 6, resulting in a new multicritical point at its meeting with the boundaries to the paramagnetic phase. In d=3,4,5, a paramagnetic phase reaching zero temperature intervenes asymmetrically between the ferromagnetic and reentrant antiferromagnetic phases. There is no spin-glass phase in any dimension.

cond-mat.dis-nn↗

arXiv2007

Field-Driven Hysteresis of the d=3 Ising Spin Glass: Hard-Spin Mean-Field Theory

Hysteresis loops are obtained in the Ising spin-glass phase in d=3, using frustration-conserving hard-spin mean-field theory. The system is driven by a time-dependent random magnetic field H_Q that is conjugate to the spin-glass order Q, yielding a field-driven first-order phase transition through the spin-glass phase. The hysteresis loop area A of the Q-H_Q curve scales with respect to the sweep rate h of magnetic field as A-A_0 = h^b. In the spin-glass and random-bond ferromagnetic phases, the sweep-rate scaling exponent b changes with temperature T, but appears not to change with antiferromagnetic bond concentration p. By contrast, in the pure ferromagnetic phase, b does not depend on T and has a sharply different value than in the two other phases.

cond-mat.dis-nn↗

arXiv2007

High-Precision Thermodynamic and Critical Properties from Tensor Renormalization-Group Flows

The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than 10^-5 along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range D) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with D = 24, corresponding to 4624-dimensional renormalization-group flows.

cond-mat.stat-mech↗

arXiv2006

d=3 Anisotropic and d=2 tJ Models: Phase Diagrams, Thermodynamic Properties, and Chemical Potential Shift

The anisotropic d=3 tJ model is studied by renormalization-group theory, yielding the evolution of the system as interplane coupling is varied from the isotropic three-dimensional to quasi-two-dimensional regimes. Finite-temperature phase diagrams, chemical potential shifts, and in-plane and interplane kinetic energies and antiferromagnetic correlations are calculated for the entire range of electron densities. We find that the novel tau phase, seen in earlier studies of the isotropic d=3 tJ model, and potentially corresponding to the superconducting phase in high-T_c materials, persists even for strong anisotropy. While the tau phase appears at low temperatures at 30-35% hole doping away from =1, at smaller hole dopings we see a complex lamellar structure of antiferromagnetic and disordered regions, with a suppressed chemical potential shift, a possible marker of incommensurate ordering in the form of microscopic stripes. An investigation of the renormalization-group flows for the isotropic two-dimensional tJ model also shows a pre-signature of the tau phase, which appears with finite transition temperatures upon addition of the smallest interplane coupling.

cond-mat.str-el↗

arXiv2006

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 with a scale-free degree distribution, high clustering coefficient, and small-world behavior. 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. We obtain analytical 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 Ising model on this network is studied through an exact renormalization-group transformation of the quenched bond probability distribution, using up to 562,500 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 T_c. For p >= 0.494, 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 non-zero magnetization and finite correlation length and a high-temperature phase with zero magnetization and infinite correlation length. Approaching T_c from below, the magnetization and the susceptibility respectively exhibit the singularities of exp(-C/sqrt(T_c-T)) and exp(D/sqrt(T_c-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, an unusually narrow critical region and important corrections to power-law behavior that depend on the exponent characterizing the decay of long-range interactions.

cond-mat.dis-nn↗

arXiv2005

Multicritical Point Relations in Three Dual Pairs of Hierarchical-Lattice Ising Spin-Glasses

The Ising spin-glasses are investigated on three dual pairs of hierarchical lattices, using exact renormalization-group transformation of the quenched bond probability distribution. The goal is to investigate a recent conjecture which relates, on such pairs of dual lattices, the locations of the multicritical points, which occur on the Nishimori symmetry line. Towards this end we precisely determine the global phase diagrams for these six hierarchical spin-glasses, using up to 2.5 x 10^9 probability bins to represent the quenched distribution subjected to an exact renormalization-group transformation. We find in all three cases that the conjecture is realized to a very good approximation, even when the mutually dual models belong to different spatial dimensionalities d and have different phase diagram topologies at the multicritical points of the conjecture and even though the contributions to the conjecture from each lattice of the dual pair are strongly asymmetric. In all six phase diagrams, we find reentrance near the multicritical point. In the models with d=2 or 1.5, the spin-glass phase does not occur and the phase boundary between the ferromagnetic and paramagnetic phases is second order with a strong violation of universality. PACS numbers: 75.10.Nr, 64.60.Kw, 05.45.Df, 05.10.Cc

cond-mat.dis-nn↗

arXiv2005

Superfluid Weight, Free Carrier Density, and Specific Heat of the d=3 tJ Model at Finite Temperatures

The superfluid weight, free carrier density, and specific heat of the three-dimensional tJ model are calculated by renormalization-group theory. We find that optimal hole doping for superfluidity occurs in the electron density range of n_i approximately between 0.63 - 0.68, where the superfluid weight n_s/m* reaches a local maximum. This density range is within the novel tau phase, where the electron hopping strength renormalizes to infinity, the system remains partially filled at all length scales, and the electron-hopping expectation value remains distinctively non-zero at all length scales. The calculated superfluid weight drops off sharply in the overdoped region. Under hole doping, the calculated density of free carriers increases until optimal doping and remains approximately constant in the overdoped region, as seen experimentally in high-T_c materials. Furthermore, from calculation of the specific heat coefficient gamma, we see clear evidence of a gap in the excitation spectrum for the tau phase.

cond-mat.str-el↗

arXiv2005

Two Superconducting Phases in the d=3 Hubbard Model: Phase Diagram and Specific Heat from Renormalization-Group Calculations

The phase diagram of the d=3 Hubbard model is calculated as a function of temperature and electron density n_i, in the full range of densities between 0 and 2 electrons per site, using renormalization-group theory. An antiferromagnetic phase occurs at lower temperatures, at and near the half-filling density of = 1. The antiferromagnetic phase is unstable to hole or electron doping of at most 15%, yielding to two distinct "tau" phases: for large coupling U/t, one such phase occurs between 30-35% hole or electron doping, and for small to intermediate coupling U/t another such phase occurs between 10-18% doping. Both tau phases are distinguished by non-zero hole or electron hopping expectation values at all length scales. Under further doping, the tau phases yield to hole- or electron-rich disordered phases. We have calculated the specific heat over the entire phase diagram. The low-temperature specific heat of the weak-coupling tau phase shows a BCS-type exponential decay, indicating a gap in the excitation spectrum, and a cusp singularity at the phase boundary. The strong-coupling tau phase, on the other hand, has characteristics of BEC-type superconductivity, including a critical exponent alpha approximately equal to -1, and an additional peak in the specific heat above the transition temperature indicating pair formation. In the limit of large Coulomb repulsion, the phase diagram of the tJ model is recovered.

cond-mat.str-el↗

arXiv2000

Multiplicity of Ordered Phases in Frustrated Systems Obtained from Hard-Spin Mean-Field Theory

Random quenched dilution of the triangular-lattice antiferromagnetic Ising model locally relieves frustration, leading to ordering phenomena. We have studied this system, under such dilution of one sublattice, using hard-spin mean-field theory. After a threshold dilution, two sublattices develop non-zero magnetizations of equal magnitude and opposite signs, as all three sublattices exhibit spin-glass order. In this phase, multiple sets of ordered solutions occur. A phase diagram is obtained in dilution fraction and temperature.

cond-mat.stat-mech↗