700 research outputs found
Strongly Asymmetric Tricriticality of Quenched Random-Field Systems
In view of the recently seen dramatic effect of quenched random bonds on
tricritical systems, we have conducted a renormalization-group study on the
effect of quenched random fields on the tricritical phase diagram of the spin-1
Ising model in . We find that random fields convert first-order phase
transitions into second-order, in fact more effectively than random bonds. The
coexistence region is extremely flat, attesting to an unusually small
tricritical exponent ; moreover, an extreme asymmetry of the phase
diagram is very striking. To accomodate this asymmetry, the second-order
boundary exhibits reentrance.Comment: revtex, 4 pages, 2 figs, submitted to PR
Multicritical points for the spin glass models on hierarchical lattices
The locations of multicritical points on many hierarchical lattices are
numerically investigated by the renormalization group analysis. The results are
compared with an analytical conjecture derived by using the duality, the gauge
symmetry and the replica method. We find that the conjecture does not give the
exact answer but leads to locations slightly away from the numerically reliable
data. We propose an improved conjecture to give more precise predictions of the
multicritical points than the conventional one. This improvement is inspired by
a new point of view coming from renormalization group and succeeds in deriving
very consistent answers with many numerical data.Comment: 11 pages, 9 figures, 7 tables This is the published versio
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.Comment: 13 pages, 7 figures; replaced with published versio
Critical Percolation Phase and Thermal BKT Transition in a Scale-Free Network with Short-Range and Long-Range Random Bonds
Percolation in a scale-free hierarchical network is solved exactly by
renormalization-group theory, in terms of the different probabilities of
short-range and long-range bonds. A phase of critical percolation, with
algebraic (Berezinskii-Kosterlitz-Thouless) geometric order, occurs in the
phase diagram, in addition to the ordinary (compact) percolating phase and the
non-percolating phase. It is found that no connection exists between, on the
one hand, the onset of this geometric BKT behavior and, on the other hand, the
onsets of the highly clustered small-world character of the network and of the
thermal BKT transition of the Ising model on this network. Nevertheless, both
geometric and thermal BKT behaviors have inverted characters, occurring where
disorder is expected, namely at low bond probability and high temperature,
respectively. This may be a general property of long-range networks.Comment: Added explanations and data. Published version. 4pages, 4 figure
ON THE LOW-TEMPERATURE ORDERING OF THE 3D ATIFERROMAGNETIC THREE-STATE POTTS MODEL
The antiferromagnetic three-state Potts model on the simple-cubic lattice is
studied using Monte Carlo simulations. The ordering in a medium temperature
range below the critical point is investigated in detail. Two different regimes
have been observed: The so-called broken sublattice-symmetry phase dominates at
sufficiently low temperatures, while the phase just below the critical point is
characterized by an effectively continuous order parameter and by a fully
restored rotational symmetry. However, the later phase is not the
permutationally sublattice symmetric phase recently predicted by the cluster
variation method.Comment: 20 pages with 9 figures in a single postscript file (compressed and
uuencoded by uufiles -gz -9) plus two big figures in postscript file
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.Comment: 16 pages, 10 figures; typos in Fig. 2 correcte
Potts-Percolation-Gauss Model of a Solid
We study a statistical mechanics model of a solid. Neighboring atoms are
connected by Hookian springs. If the energy is larger than a threshold the
"spring" is more likely to fail, while if the energy is lower than the
threshold the spring is more likely to be alive. The phase diagram and
thermodynamic quantities, such as free energy, numbers of bonds and clusters,
and their fluctuations, are determined using renormalization-group and
Monte-Carlo techniques.Comment: 10 pages, 12 figure
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.Comment: New results added to text and figures. 12 pages, 18 figures, 3
tables. Published versio
Phase Diagrams and Crossover in Spatially Anisotropic d=3 Ising, XY Magnetic and Percolation Systems: Exact Renormalization-Group Solutions of Hierarchical Models
Hierarchical lattices that constitute spatially anisotropic systems are
introduced. These lattices provide exact solutions for hierarchical models and,
simultaneously, approximate solutions for uniaxially or fully anisotropic d=3
physical models. The global phase diagrams, with d=2 and d=1 to d=3 crossovers,
are obtained for Ising, XY magnetic models and percolation systems, including
crossovers from algebraic order to true long-range order.Comment: 7 pages, 12 figures. Corrected typos, added publication informatio
Random site dilution properties of frustrated magnets on a hierarchical lattice
We present a method to analyze magnetic properties of frustrated Ising spin
models on specific hierarchical lattices with random dilution. Disorder is
induced by dilution and geometrical frustration rather than randomness in the
internal couplings of the original Hamiltonian. The two-dimensional model
presented here possesses a macroscopic entropy at zero temperature in the large
size limit, very close to the Pauling estimate for spin-ice on pyrochlore
lattice, and a crossover towards a paramagnetic phase. The disorder due to
dilution is taken into account by considering a replicated version of the
recursion equations between partition functions at different lattice sizes. An
analysis at first order in replica number allows for a systematic
reorganization of the disorder configurations, leading to a recurrence scheme.
This method is numerically implemented to evaluate the thermodynamical
quantities such as specific heat and susceptibility in an external field.Comment: 26 pages, 11 figure
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