Random network models with variable disorder of geometry

Klümper, Andreas; Nuding, W.; Sedrakyan, A.

doi:10.1103/physrevb.100.140201

Cited by 35 publications

(43 citation statements)

References 54 publications

(89 reference statements)

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“…In the 1D limit a 2D magnet splits into a set of independent 1D magnets that are completely isolated from each other. For each 1D magnet the 1D Heisenberg model for spin-1/2 can be diagonalised exactly using Bethe ansatz [28] and the heat capacity can also be evaluated using this diagonalisation procedure without any approximation [29,30]. The exact result reproduces quite well the J /J = 0 curve in Fig.…”

Section: Thermodynamicsmentioning

confidence: 78%

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Heat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D regime

2019

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We study the anisotropic quantum Heisenberg antiferromagnet for spin-1/2 that interpolates smoothly between the one-dimensional (1D) and the two-dimensional (2D) limits. Using the spin Hartree-Fock approach we construct a quantitative theory of heat capacity in the quasi-1D regime with a finite coupling between spin chains. This theory reproduces closely the exact result of Bethe Ansatz in the 1D limit and does not produces any spurious phase transitions for any anisotropy in the quasi-1D regime at finite temperatures in agreement with the Mermin-Wagner theorem. We study the static spin-spin correlation function in order to analyse the interplay of lattice geometry and anisotropy in these systems. We compare the square and triangular lattice. For the latter we find that there is a quantum transition point at an intermediate anisotropy of ∼ 0.6. This quantum phase transition establishes that the quasi-1D regime extends upto a particular point in this geometry. For the square lattice the change from the 1D to 2D occurs smoothly as a function of anisotropy, i.e. it is of the crossover type. Comparing the newly developed theory to the available experimental data on the heat capacity of Cs2CuBr4 and Cs2CuCl4 we extract the microscopic constants of the exchange interaction that previously could only be measured using inelastic neutron scattering in high magnetic fields. arXiv:1911.09403v1 [cond-mat.str-el]

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Section: Thermodynamicsmentioning

confidence: 78%

“…(26). The dash-dotted line is the result of Bethe ansatz from [30]. where u 1 ≡ u x and u 2 ≡ u y are now the variables in the orthogonal directions of the primitive vectors of the square lattice and V = (2π) 2 is the volume of the primitive cell in the reciprocal space of the square lattice.…”

Section: Square Latticementioning

confidence: 99%

Heat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D regime

2019

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“…The authors acknowledge helpful discussions with E Agliari, E Barkai, S Redner and A Gorsky, and also wish to thank the latter for pointing us on [38].…”

Section: Acknowledgmentsmentioning

confidence: 98%

“…[37]). A generalisation of a random Manhattan lattice was invoked as an example of a plausible geometric disorder in a recent analysis of the localisation length exponent for plateau transition in quantum Hall effect [38]. This latter setting, however, is clearly more complicated than the MdM model with the layered flows and the theoretical progress here is rather limited; the behaviour beyond the temporal evolution of a DA MSD is still largely unknown.…”

Section: Introductionmentioning

confidence: 99%

Tracer diffusion on a crowded random Manhattan lattice

et al. 2020

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We study, by extensive numerical simulations, the dynamics of a hard-core tracer particle (TP) in presence of two competing types of disorder-frozen convection flows on a square random Manhattan lattice and a crowded dynamical environment formed by a lattice gas of mobile hard-core particles. The latter perform lattice random walks, constrained by a single-occupancy condition of each lattice site, and are either insensitive to random flows (model A) or choose the jump directions as dictated by the local directionality of bonds of the random Manhattan lattice (model B). We focus on the TP disorder-averaged mean-squared displacement, (which shows a super-diffusive behaviour ∼t 4/3 , t being time, in all the cases studied here), on higher moments of the TP displacement, and on the probability distribution of the TP position X along the x-axis, for which we unveil a previously unknown behaviour. Indeed, our analysis evidences that in absence of the lattice gas particles the latter probability distribution has a Gaussian central part ( ) -u exp 2 , where u=X/t 2/3 , and exhibits slower-than-Gaussian tails ( | | ) u exp 4 3 for sufficiently large t and u. Numerical data convincingly demonstrate that in presence of a crowded environment the central Gaussian part and non-Gaussian tails of the distribution persist for both models.

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“…with Ω = J and the contribution c H of the isotropic Heisenberg model 16 . As can be clearly seen the Einstein phonons are dominant at high temperatures, in particular the constancy of the specific heat, as expected according to the Dulong-Petit rule, is visible.…”

Section: B Specific Heat Phonon Occupation Numbermentioning

confidence: 99%

Thermodynamical Properties of a Spin 1/2 Heisenberg Chain Coupled to Phonons

Kühne¹

2019

Preprint

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We performed a finite-temperature quantum Monte Carlo simulation of the one-dimensional spin-1 2 Heisenberg model with nearest-neighbor interaction coupled to Einstein phonons. Our method allows to treat easily up to 100 phonons per site and the results presented are practically free from truncation errors. We studied in detail the magnetic susceptibility, the specific heat, the phonon occupation, the dimerization, and the spin-correlation function for various spin-phonon couplings and phonon frequencies. In particular we give evidence for the transition from a gapless to a massive phase by studying the finite-size behavior of the susceptibility. We also show that the dimerization is proportional to g 2 /Ω for T < 2J.

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Random network models with variable disorder of geometry

Cited by 35 publications

References 54 publications

Heat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D regime

Heat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D regime

Tracer diffusion on a crowded random Manhattan lattice

Thermodynamical Properties of a Spin 1/2 Heisenberg Chain Coupled to Phonons

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