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

Physica A Statistical Mechanics and its Applications

A renormalization group calculation of the swelling factor for a non-ideal, randomly jointed polymer chain

Andrzej R. Altenberger, Joern Ilja Siepmann, John S. Dahler

Published Oct 1, 1999• 4 citations
Publisher
DOI
10.1016/s0378-4371(99)00236-8

Related papers

On the direct renormalization group procedure for a polymer chain

Alexander Y. Grosberg, Igor Ya. Erukhimovich, Alexei R. Khokhlov

Physics Letters A•Jul 1, 1980•4 citations

Position-Space Renormalization Group for Models of Linear Polymers, Branched Polymers, and Gels

Eugene Stanley, PETER J. REYNOLDS, S. Redner +1 more

Topics in current physics•Jan 1, 1982•20 citations

Improved matrix product operator renormalization group: application to the N -color random Ashkin–Teller chain

Christophe Chatelain

Abstract Strong-disorder renormalization group (SDRG), despite being a relatively simple real-space renormalization procedure, provides in principle exact results on the critical properties at the infinite-randomness fixed point of random quantum spin chains. Numerically, SDRG can be efficiently implemented as a renormalization of matrix product operators (MPO-RG). By considering larger blocks than SDRG, MPO-RG was recently used to compute non-critical quantities of finite chains that are inaccessible to SDRG. In this work, the accuracy of this approach is studied and two simple and fast improvements are proposed. The accuracy on the ground state energy is improved by a factor at least equal to four for the random Ising chain in a transverse field. Finally, the proposed algorithms are shown to yield Binder cumulants of the three-color random Ashkin–Teller chain that are compatible with a second-order phase transition while a first-order one is predicted by the original MPO-RG algorithm.

arXiv:1807.08984•Journal of Statistical Mechanics Theory and Experiment•Sep 1, 2019•2 citations

Quantifying and improving the accuracy of the Matrix Product Operator Renormalization Group of random spin chains

Christophe Chatelain

A relatively simple real-space renormalization procedure, due to Ma and Dasgupta and known as Strong-Disorder Renormalization Group (SDRG), provides in principle exact results on the critical properties at the infinite-randomness fixed point of random spin chains. Numerically, SDRG can be efficiently implemented as a renormalization of Matrix Product Operators (MPO-RG). By considering larger blocks than SDRG, MPO-RG was recently used to compute non-critical quantities that are inaccessible to SDRG. In this work, we study the accuracy of the approach and propose two simple and fast improvements. We observe that the accuracy on the ground state energy is improved by a factor at least equal to 4.

•Jul 19, 2018•1 citation

Functional Renormalization Group of Disordered Systems

Taiki Haga

Springer theses•Jan 1, 2019•0 citations

RENORMALIZATION-GROUP INVESTIGATION OF THE S = 1 RANDOM ANTIFERROMAGNETIC HEISENBERG CHAIN

Péter Lajkó

We introduce variants of the Ma-Dasgupta renormalization-group (RG) approach for random quantum spin chains, in which the energy-scale is reduced by decimation built on either perturbative or non-perturbative principles. In one non-perturbative version of the method, we require the exact invariance of the lowest gaps, while in a second class of perturbative Ma-Dasgupta techniques, different decimation rules are utilized. For the S = 1 random antiferromagnetic Heisenberg chain, both type of methods provide the same type of disorder dependent phase diagram, which is in agreement with density-matrix renormalization-group calculations and previous studies.

arXiv:0903.0462•International Journal of Modern Physics C•Dec 1, 2006•1 citation
Abstract Strong-disorder renormalization group (SDRG), despite being a relatively simple real-space renormalization procedure, provides in principle exact results on the critical properties at the infinite-randomness fixed point of random quantum spin chains. Numerically, SDRG can be efficiently implemented as a renormalization of matrix product operators (MPO-RG). By considering larger blocks than SDRG, MPO-RG was recently used to compute non-critical quantities of finite chains that are inaccessible to SDRG. In this work, the accuracy of this approach is studied and two simple and fast improvements are proposed. The accuracy on the ground state energy is improved by a factor at least equal to four for the random Ising chain in a transverse field. Finally, the proposed algorithms are shown to yield Binder cumulants of the three-color random Ashkin–Teller chain that are compatible with a second-order phase transition while a first-order one is predicted by the original MPO-RG algorithm.
A relatively simple real-space renormalization procedure, due to Ma and Dasgupta and known as Strong-Disorder Renormalization Group (SDRG), provides in principle exact results on the critical properties at the infinite-randomness fixed point of random spin chains. Numerically, SDRG can be efficiently implemented as a renormalization of Matrix Product Operators (MPO-RG). By considering larger blocks than SDRG, MPO-RG was recently used to compute non-critical quantities that are inaccessible to SDRG. In this work, we study the accuracy of the approach and propose two simple and fast improvements. We observe that the accuracy on the ground state energy is improved by a factor at least equal to 4.
We introduce variants of the Ma-Dasgupta renormalization-group (RG) approach for random quantum spin chains, in which the energy-scale is reduced by decimation built on either perturbative or non-perturbative principles. In one non-perturbative version of the method, we require the exact invariance of the lowest gaps, while in a second class of perturbative Ma-Dasgupta techniques, different decimation rules are utilized. For the S = 1 random antiferromagnetic Heisenberg chain, both type of methods provide the same type of disorder dependent phase diagram, which is in agreement with density-matrix renormalization-group calculations and previous studies.