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

Scaling function for two-point correlations with long-range interactions to order 1/η

W. K. Theumann

Published Jan 1, 1976• 2 citations
Publisher
DOI
10.1016/0378-4371(76)90137-0

Related papers

Critical scaling function for long-range interactions to order 1/n

W. K. Theumann

Physics Letters A•Jul 1, 1975•2 citations

Long-range random-field models: scaling theory and 1/n expansion

Alan J. Bray

Random-field models are considered with long-range exchange, J(r) approximately 1/r d+ sigma , and/or long-range correlated random fields, (h(r)h(r')) approximately 1/ mod r-r' mod d- rho . A general scaling analysis is presented, in which the existence of three independent critical exponents is emphasized. Four different universality classes are identified, according to whether the fixed point controlling the critical behaviour is of short-range or long-range character for the exchange and/or the random-field correlations. The lines in the rho - sigma plane at which the long-range couplings first become relevant are expressed in terms of the exponents eta and eta of the corresponding short-range problem: long-range exchange is relevant for sigma <2- eta , long-range field correlations for rho >2 eta - eta . The scaling results are confirmed and amplified by explicit calculations of three independent exponents of the n-component spin model, correct to order 1/n. The results reveal errors in published expansions around the upper critical dimension.

Journal of Physics C Solid State Physics•Nov 10, 1986•25 citations

Renormalization group for the φ4 theory with long-range interaction and the critical exponent η of the Ising model

Raphael Goll, Peter Kopietz

We calculate the critical exponent η of the D-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction. Our approach relies on the smallness of the inverse range of the interaction and on the assumption that the Ginzburg momentum defining the width of the scaling regime in momentum space is larger than the scale where the renormalized interaction crosses over from long range to short range; the numerical value of η can then be estimated by stopping the renormalization group flow at this scale. In three dimensions our result η=0.03651 is in good agreement with recent conformal bootstrap and Monte Carlo calculations. We extend our calculations to fractional dimensions D and obtain the resulting critical exponent η(D) between two and four dimensions. For dimensions 2≤D≤3 our result for η is consistent with previous calculations.

arXiv:1804.04150•Physical review. E•Aug 28, 2018•6 citations

Scaling Function for Order-Parameter Correlations in Expansion to Order 1/N. 1. Short Range Interactions

W. K. Theumann

Physical review. D/Physical review. D.•Jan 1, 1974•0 citations

Entanglement and off-diagonal long-range order of an η-pairing state

Heng Fan, Seth Lloyd

Off-diagonal long-range order (ODLRO) which is believed to be one characteristic of superconductivity is a quantum phenomenon not describable in classical mechanical terms. The quantum state constructed by η-pairing demonstrates ODLRO. Entanglement is a key concept of the quantum information processing and has no classical counterpart. We study the entanglement property of the η-pairing quantum state by concurrence and entropy which are two measures of the entanglement. We show that the concurrence of entanglement between one-site and the rest sites is exactly the correlation function of the ODLRO for the η-pairing state in the thermodynamic limit. So, when the η-pairing state is entangled, it demonstrates ODLRO and is thus in the superconducting phase, if it is a separable state, there is no ODLRO. In the thermodynamical limit, the entanglement between the M -site and other sites of the η-pairing state does not vanish. Other types of ODLRO of the η-pairing state are presented. We show that the behaviour of the ODLRO correlation functions is equivalent to that of the entanglement of the η-pairing state. The scaling of the entropy of the entanglement for the η-pairing state is studied.

arXiv:quant-ph/0405130•Journal of Physics A Mathematical and General•May 25, 2005•25 citations

Scaling function for order-parameter correlations in expansion to order 1/n

W. K. Theumann

Physica A Statistical Mechanics and its Applications•Jan 1, 1975•2 citations
Random-field models are considered with long-range exchange, J(r) approximately 1/r d+ sigma , and/or long-range correlated random fields, (h(r)h(r')) approximately 1/ mod r-r' mod d- rho . A general scaling analysis is presented, in which the existence of three independent critical exponents is emphasized. Four different universality classes are identified, according to whether the fixed point controlling the critical behaviour is of short-range or long-range character for the exchange and/or the random-field correlations. The lines in the rho - sigma plane at which the long-range couplings first become relevant are expressed in terms of the exponents eta and eta of the corresponding short-range problem: long-range exchange is relevant for sigma <2- eta , long-range field correlations for rho >2 eta - eta . The scaling results are confirmed and amplified by explicit calculations of three independent exponents of the n-component spin model, correct to order 1/n. The results reveal errors in published expansions around the upper critical dimension.
We calculate the critical exponent η of the D-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction. Our approach relies on the smallness of the inverse range of the interaction and on the assumption that the Ginzburg momentum defining the width of the scaling regime in momentum space is larger than the scale where the renormalized interaction crosses over from long range to short range; the numerical value of η can then be estimated by stopping the renormalization group flow at this scale. In three dimensions our result η=0.03651 is in good agreement with recent conformal bootstrap and Monte Carlo calculations. We extend our calculations to fractional dimensions D and obtain the resulting critical exponent η(D) between two and four dimensions. For dimensions 2≤D≤3 our result for η is consistent with previous calculations.
Off-diagonal long-range order (ODLRO) which is believed to be one characteristic of superconductivity is a quantum phenomenon not describable in classical mechanical terms. The quantum state constructed by η-pairing demonstrates ODLRO. Entanglement is a key concept of the quantum information processing and has no classical counterpart. We study the entanglement property of the η-pairing quantum state by concurrence and entropy which are two measures of the entanglement. We show that the concurrence of entanglement between one-site and the rest sites is exactly the correlation function of the ODLRO for the η-pairing state in the thermodynamic limit. So, when the η-pairing state is entangled, it demonstrates ODLRO and is thus in the superconducting phase, if it is a separable state, there is no ODLRO. In the thermodynamical limit, the entanglement between the M -site and other sites of the η-pairing state does not vanish. Other types of ODLRO of the η-pairing state are presented. We show that the behaviour of the ODLRO correlation functions is equivalent to that of the entanglement of the η-pairing state. The scaling of the entropy of the entanglement for the η-pairing state is studied.