Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9808027 · Physical review. B, Condensed matter

Thermodynamics of random ferromagnetic-antiferromagnetic spin-1/2 chains

Beat Frischmuth, Manfred Sigrist, Beat Ammon, Matthias Troyer

Published Aug 1, 1999• 22 citations
arXivHTMLPDF

Abstract

Using the quantum Monte Carlo loop algorithm, we calculate the temperature dependence of the uniform susceptibility, the specific heat, the correlation length, the generalized staggered susceptibility, and magnetization of a spin-1/2 chain with random antiferromagnetic and ferromagnetic couplings, down to very low temperatures. Our data show a consistent scaling behavior in all the quantities and support strongly the conjecture drawn from the approximate real-space renormalization group treatment. A statistical analysis scheme is developed which will be useful for the search of scaling behavior in numerical and experimental data of random spin chains.

DOI
10.1103/physrevb.60.3388

Related papers

Low-Temperature Scaling Regime of Random Ferromagnetic-Antiferromagnetic Spin Chains

Beat Frischmuth, Manfred Sigrist

Using the continuous time quantum Monte Carlo loop algorithm, we calculate the temperature dependence of the uniform susceptibility, and the specific heat of a spin-1/2 chain with random antiferromagnetic and ferromagnetic couplings, down to very low temperatures. Our data show a consistent scaling behavior in both quantities and strongly support the conjecture drawn from the approximative real-space renormalization group treatment. A statistical analysis scheme is developed which will be useful for the search of scaling behavior in numerical and experimental data of random spin chains.

arXiv:cond-mat/9702215•Physical Review Letters•Jul 7, 1997•17 citations

Monte Carlo Study of the Separation of Energy Scales in Quantum Spin 1/2 Chains with Bond Disorder

Beat Ammon, Manfred Sigrist

One-dimensional Heisenberg spin 1/2 chains with random ferro- and antiferromagnetic bonds are realized in systems such as $Sr_3 CuPt_{1-x} Ir_x O_6$. We have investigated numerically the thermodynamic properties of a generic random bond model and of a realistic model of $Sr_3 CuPt_{1-x} Ir_x O_6$ by the quantum Monte Carlo loop algorithm. For the first time we demonstrate the separation into three different temperature regimes for the original Hamiltonian based on an exact treatment, especially we show that the intermediate temperature regime is well-defined and observable in both the specific heat and the magnetic susceptibility. The crossover between the regimes is indicated by peaks in the specific heat. The uniform magnetic susceptibility shows Curie-like behavior in the high-, intermediate- and low-temperature regime, with different values of the Curie constant in each regime. We show that these regimes are overlapping in the realistic model and give numerical data for the analysis of experimental tests.

arXiv:cond-mat/9902252•Journal of the Physical Society of Japan•Mar 15, 1999•6 citations

Random exchange effects in antiferromagnetic quantum spin chains: A Monte Carlo study

H.-B. Schüttler, Douglas J. Scalapino, Paul Michael Grant

We have carried out Monte Carlo studies of a random-exchange antiferromagnetic spin-(1/2) chain. For systems with XY-like (anisotropic) and with Heisenberg (isotropic) coupling, our results confirm the existence of a disorder-induced low-temperature (T) divergence in the long-wavelength ${S}^{z}$-${S}^{z}$ susceptibility \ensuremath{\chi} which was previously predicted by real-space renormalization-group (RSRG) treatments. Over the finite temperature range studied, these results are consistent with a 1/(T ${\mathrm{ln}}^{2}$T) behavior of \ensuremath{\chi}, and hence in qualitative agreement with the RSRG results. As in the XY-Heisenberg regime, we also find a disorder-induced enhancement of the low-T susceptibility for a system with Ising-like exchange coupling which, over the finite temperature range studied, is again consistent with RSRG results. However, there are inconsistencies between the RSRG predictions in the Ising-like regime at very low temperatures, and the exact results for the random-exchange Ising chain and the low-temperature behavior of \ensuremath{\chi} in the Ising-like regime may in fact be more complicated than predicted by RSRG. Finally, we also present results for the antiferromagnetic susceptibility and structure factor. For both Heisenberg and Ising-like systems, we find that disorder suppresses the long-range antiferromagnetic correlations at low T.

Physical review. B, Condensed matter•Mar 1, 1987•8 citations

Low Energy Properties of the Random Spin-1/2 Ferromagnetic-Antiferromagnetic Heisenberg Chain

Kazuo Hida

The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet phase and the formation of the large-spin state is observed even for relatively small systems. For a small fraction of the ferromagnetic bond, the effect of the crossover to the random singlet phase on the low temperature susceptibility and specific heat is discussed. The crossover concentration of the ferromagnetic bond is estimated from the numerical data.

arXiv:cond-mat/9612232•Journal of the Physical Society of Japan•Feb 15, 1997•16 citations

Thermodynamics of quantum Heisenberg spin chains

Tao Xiang

Thermodynamic properties of the quantum Heisenberg spin chains with $S=1/2,$ 1, and $3/2$ are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.

arXiv:cond-mat/9808179•Physical review. B, Condensed matter•Oct 1, 1998•92 citations

Numerical renormalization-group study of spin correlations in one-dimensional random spin chains

Takashi Hikihara, Akira Furusaki, Manfred Sigrist

We calculate the ground-state two-spin correlation functions of spin-$\frac{1}{2}$ quantum Heisenberg chains with random exchange couplings using the real-space renormalization-group scheme. We extend the conventional scheme to take account of the contribution of local higher multiplet excitations in each decimation step. This extended scheme can provide highly accurate numerical data for large systems. The random average of staggered spin correlations of the chains with random antiferromagnetic (AF) couplings shows algebraic decay like ${1/r}^{2},$ which verifies the Fisher's analytic results. For chains with random ferromagnetic (FM) and AF couplings, the random average of generalized staggered correlations is found to decay more slowly than a power law, in the form close to $1/\mathrm{ln}(r).$ The difference between the distribution functions of the spin correlations of the random AF chains and of the random FM-AF chains is also discussed.

arXiv:cond-mat/9905352•Physical review. B, Condensed matter•Nov 1, 1999•40 citations
Using the quantum Monte Carlo loop algorithm, we calculate the temperature dependence of the uniform susceptibility, the specific heat, the correlation length, the generalized staggered susceptibility, and magnetization of a spin-1/2 chain with random antiferromagnetic and ferromagnetic couplings, down to very low temperatures. Our data show a consistent scaling behavior in all the quantities and support strongly the conjecture drawn from the approximate real-space renormalization group treatment. A statistical analysis scheme is developed which will be useful for the search of scaling behavior in numerical and experimental data of random spin chains.
Using the continuous time quantum Monte Carlo loop algorithm, we calculate the temperature dependence of the uniform susceptibility, and the specific heat of a spin-1/2 chain with random antiferromagnetic and ferromagnetic couplings, down to very low temperatures. Our data show a consistent scaling behavior in both quantities and strongly support the conjecture drawn from the approximative real-space renormalization group treatment. A statistical analysis scheme is developed which will be useful for the search of scaling behavior in numerical and experimental data of random spin chains.
One-dimensional Heisenberg spin 1/2 chains with random ferro- and antiferromagnetic bonds are realized in systems such as Sr3CuPt1−xIrxO6Sr_3 CuPt_{1-x} Ir_x O_6Sr3​CuPt1−x​Irx​O6​. We have investigated numerically the thermodynamic properties of a generic random bond model and of a realistic model of Sr3CuPt1−xIrxO6Sr_3 CuPt_{1-x} Ir_x O_6Sr3​CuPt1−x​Irx​O6​ by the quantum Monte Carlo loop algorithm. For the first time we demonstrate the separation into three different temperature regimes for the original Hamiltonian based on an exact treatment, especially we show that the intermediate temperature regime is well-defined and observable in both the specific heat and the magnetic susceptibility. The crossover between the regimes is indicated by peaks in the specific heat. The uniform magnetic susceptibility shows Curie-like behavior in the high-, intermediate- and low-temperature regime, with different values of the Curie constant in each regime. We show that these regimes are overlapping in the realistic model and give numerical data for the analysis of experimental tests.
We have carried out Monte Carlo studies of a random-exchange antiferromagnetic spin-(1/2) chain. For systems with XY-like (anisotropic) and with Heisenberg (isotropic) coupling, our results confirm the existence of a disorder-induced low-temperature (T) divergence in the long-wavelength Sz{S}^{z}Sz-Sz{S}^{z}Sz susceptibility \ensuremath{\chi} which was previously predicted by real-space renormalization-group (RSRG) treatments. Over the finite temperature range studied, these results are consistent with a 1/(T ln2{\mathrm{ln}}^{2}ln2T) behavior of \ensuremath{\chi}, and hence in qualitative agreement with the RSRG results. As in the XY-Heisenberg regime, we also find a disorder-induced enhancement of the low-T susceptibility for a system with Ising-like exchange coupling which, over the finite temperature range studied, is again consistent with RSRG results. However, there are inconsistencies between the RSRG predictions in the Ising-like regime at very low temperatures, and the exact results for the random-exchange Ising chain and the low-temperature behavior of \ensuremath{\chi} in the Ising-like regime may in fact be more complicated than predicted by RSRG. Finally, we also present results for the antiferromagnetic susceptibility and structure factor. For both Heisenberg and Ising-like systems, we find that disorder suppresses the long-range antiferromagnetic correlations at low T.
The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet phase and the formation of the large-spin state is observed even for relatively small systems. For a small fraction of the ferromagnetic bond, the effect of the crossover to the random singlet phase on the low temperature susceptibility and specific heat is discussed. The crossover concentration of the ferromagnetic bond is estimated from the numerical data.
Thermodynamic properties of the quantum Heisenberg spin chains with S=1/2,S=1/2,S=1/2, 1, and 3/23/23/2 are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.
We calculate the ground-state two-spin correlation functions of spin-12\frac{1}{2}21​ quantum Heisenberg chains with random exchange couplings using the real-space renormalization-group scheme. We extend the conventional scheme to take account of the contribution of local higher multiplet excitations in each decimation step. This extended scheme can provide highly accurate numerical data for large systems. The random average of staggered spin correlations of the chains with random antiferromagnetic (AF) couplings shows algebraic decay like 1/r2,{1/r}^{2},1/r2, which verifies the Fisher's analytic results. For chains with random ferromagnetic (FM) and AF couplings, the random average of generalized staggered correlations is found to decay more slowly than a power law, in the form close to 1/ln(r).1/\mathrm{ln}(r).1/ln(r). The difference between the distribution functions of the spin correlations of the random AF chains and of the random FM-AF chains is also discussed.