A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
The complexity of approximating complex-valued Ising and Tutte partition functions
[article]

2017
*
arXiv
*
pre-print

We study

arXiv:1409.5627v4
fatcat:vzlt7m7gx5cu7k45gnabaxvjoq
*the**complexity**of**approximately*evaluating*the**Ising**and**Tutte**partition**functions*with*complex*parameters. ...*The*motivation for this paper*is*to study more comprehensively*the**complexity**of*(classically)*approximating**the**Ising**and**Tutte**partition**functions*with*complex*parameters. ... Acknowledgements We thank Dan Shepherd*and*Mark Jerrum for useful discussions. ...##
###
The Complexity of Approximating complex-valued Ising and Tutte partition functions

2017
*
Computational Complexity
*

We study

doi:10.1007/s00037-017-0162-2
fatcat:whewokm6sbdqhpzsn47bwpym2e
*the**complexity**of**approximately*evaluating*the**Ising**and**Tutte**partition**functions*with*complex*parameters. ...*The*motivation for this paper*is*to study more comprehensively*the**complexity**of*(classically)*approximating**the**Ising**and**Tutte**partition**functions*with*complex*parameters. ... BQP*and**the**Tutte*polynomial Bordewich et al. [4] raised*the*question "*of*determining whether*the**Tutte*polynomial*is*greater than or equal to, or less than zero at a given point." ...##
###
Approximating the partition function of the ferromagnetic potts model

2012
*
Journal of the ACM
*

Specifically we show that

doi:10.1145/2371656.2371660
fatcat:5o5ql5h3bvez3k6vwcxyrtrtcq
*the**partition**function**is*hard for*the**complexity*class #RHPi_1 under*approximation*-preserving reducibility. ... Thus, it*is*as hard to*approximate**the**partition**function*as it*is*to find*approximate*solutions to a wide range*of*counting problems, including that*of*determining*the*number*of*independent sets in a ... As formulated in (2) ,*the**Tutte*polynomial*is**the**partition**function**of*this model. ...##
###
A little statistical mechanics for the graph theorist

2010
*
Discrete Mathematics
*

We discuss

doi:10.1016/j.disc.2010.03.011
fatcat:roiu7evabzg3bojnbvhl56ebdm
*the*equivalence*of**the*chromatic polynomial*and**the*zero-temperature antiferromagnetic*partition**function*,*and*how this has led to*the*study*of**the**complex*zeros*of*these*functions*. ... We present*the*surprising equivalence*of**the*Potts model*partition**function**and*one*of**the*most renowned graph invariants,*the**Tutte*polynomial, a relationship that has resulted in a remarkable synergy ... What*is**the*relationship between*the*Potts model*and**the*chromatic polynomial? What*is**the*computational*complexity**of**the**partition**function*? ...##
###
The Tutte–Potts connection in the presence of an external magnetic field

2011
*
Advances in Applied Mathematics
*

We prove that

doi:10.1016/j.aam.2011.02.004
fatcat:qvbj4cnjxnehdiwq4ogudltvpa
*the*variable field Potts model*partition**function*(with its many specializations)*is*an evaluation*of**the*V-polynomial,*and*hence a polynomial with deletion-contraction reduction*and*Fortuin-Kasteleyn ...*The*classical relationship between*the**Tutte*polynomial*of*graph theory*and**the*Potts model*of*statistical mechanics has resulted in valuable interactions between*the*disciplines. ... Acknowledgments We thank Alain Brizard, Leslie Ann Goldberg, Maria Kiskowski, Steve Noble, Robert Shrock, Jim Stasheff,*and*especially Alan Sokal, for several informative conversations. ...##
###
Deterministic Polynomial-Time Approximation Algorithms for Partition Functions and Graph Polynomials

2017
*
SIAM journal on computing (Print)
*

In particular, our approach works for

doi:10.1137/16m1101003
fatcat:3eur4cw3rfdtvcesbo55vc6kjm
*the**Tutte*polynomial*and*independence polynomial, as well as*partition**functions**of**complex*-*valued*spin*and*edge-coloring models. ... More specifically, we define a large class*of*graph polynomials C*and*show that if p∈ C*and*there*is*a disk D centered at zero in*the**complex*plane such that p(G) does not vanish on D for all bounded degree ... Acknowledgements We thank Alexander Barvinok for stimulating discussions, useful remarks*and*for sharing*the*results in [6] with us. We thank Andreas Galanis for informing us about [42] . ...##
###
The Complexity of Approximating the Complex-Valued Potts Model

2020
*
International Symposium on Mathematical Foundations of Computer Science
*

We study

doi:10.4230/lipics.mfcs.2020.36
dblp:conf/mfcs/GalanisGH20
fatcat:ux7zybhsxvgezohy5puqoseeem
*the**complexity**of**approximating**the**partition**function**of**the*q-state Potts model*and**the*closely related*Tutte*polynomial for*complex**values**of**the*underlying parameters. ... precisely*the*location*of*zeros,*is*strongly connected with*the**complexity**of**the**approximation*problem, even for positive real-*valued*parameters. ... Hence, we can translate our results on*the**complexity**of**approximating**the**Tutte*polynomial*of*a planar graph to*the**complexity**of**approximating**the*Jones polynomial*of*an alternating link,*and*obtain ...##
###
Stability-to-instability transition in the structure of large-scale networks

2012
*
Physical Review E
*

Given

doi:10.1103/physreve.86.066106
pmid:23368003
fatcat:aarsvkj55nhuzpk77fsjarjfx4
*the*relation between*Tutte**and*Jones polynomials, our results further suggest a link between*the*above*complexity*transitions*and*transitions associated with random knots. ... We examine phase transitions between*the*easy, hard,*and**the*unsolvable phases when attempting to identify structure in large*complex*networks (community detection) in*the*presence*of*disorder induced ... Tran,*and*L. Zdeborová for discussions*and*ongoing work. ...##
###
Approximating the Tutte polynomial of a binary matroid and other related combinatorial polynomials

2013
*
Journal of computer and system sciences (Print)
*

We consider

doi:10.1016/j.jcss.2012.04.005
fatcat:xtdnriwx6bdavpaoft64sk3cvy
*the*problem*of**approximating*certain combinatorial polynomials. First, we consider*the*problem*of**approximating**the**Tutte*polynomial*of*a binary matroid with parameters q>= 2*and*gamma. ... For binary matroids, we extend this result by showing (i) there*is*no FPRAS in*the*region gamma<-2 unless NP=RP,*and*(ii) in*the*region gamma>0,*the**approximation*problem*is*hard for*the**complexity*class ... (5)*and*(6) in*the*case q = 2 to see how they both arise as natural generalisations*of**the**Ising**partition**function**of*a graph. ...##
###
The number of link and cluster states: the core of the 2Dqstate Potts model

2005
*
Journal of Physics A: Mathematical and General
*

A key element

doi:10.1088/0305-4470/38/50/002
fatcat:rayvb4gjrfgnbissm3dliop3n4
*of**the*Random Cluster representation*is**the*combinatorial factor Γ_G(,), which*is**the*number*of*ways to form distinct clusters, consisting*of*totally edges. ... Due to Fortuin*and*Kastelyin*the*q state Potts model has a representation as a sum over random graphs, generalizing*the*Potts model to arbitrary q*is*based on this representation. ... Zeros in*the**complex*q plane*The*formulation*of**the**partition**function*as a polynomial in q allows for quite easy evaluation*of**the*zeros*of**the**partition**function*in*the**complex*q plane. ...##
###
Quantum Computation and the Evaluation of Tensor Networks

2010
*
SIAM journal on computing (Print)
*

We use this algorithm to derive new quantum algorithms that

doi:10.1137/080739379
fatcat:ewqkttj5t5cnzbdspmu5vsznly
*approximate**the**partition**function**of*a variety*of*classical statistical mechanics models, including*the*Potts model. ... We present a quantum algorithm that additively*approximates**the**value**of*a tensor network to a certain scale. ... Acknowledgments We would like to thank Maarten van den Nest, Wolfgang Dür*and*Hans Briegel for pointing our attention to an implicit quantum algorithm for*the*evaluation*of**the**partition**function**of**the*...##
###
Inapproximability of the Tutte polynomial of a planar graph

2012
*
Computational Complexity
*

Vertigan completely mapped

doi:10.1007/s00037-012-0046-4
fatcat:cw3pgnkrezemfk32fpyce4xuh4
*the**complexity**of*exactly computing*the**Tutte*polynomial*of*a planar graph. ... We study*the**complexity**of**the*following problem, for rationals x*and*y: given as input a planar graph G, determine T(G;x,y). ...*The*hyperbola H 2*is**of*particular interest, as*the**Tutte*polynomial here corresponds to*the**partition**function**of**the*celebrated*Ising*model in statistical physics. ...##
###
On the algebraic complexity of some families of coloured Tutte polynomials

2004
*
Advances in Applied Mathematics
*

Generalising

doi:10.1016/s0196-8858(03)00087-3
fatcat:4ui5xgsqzffilkh4valptjqr74
*the*well-known relationship between*the**Tutte*polynomial*and**the**partition**function*from*the**Ising*model, we establish a reduction from*the*permanent to*the*coloured*Tutte*polynomial, thus ... We investigate*the*coloured*Tutte*polynomial in Valiant's algebraic framework*of*NP-completeness. ... We also thank*the*anonymous referee for some useful comments*and*suggestions. ...##
###
On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers

2008
*
Communications in Mathematical Physics
*

This problem

doi:10.1007/s00220-008-0438-0
fatcat:y5o7g27mr5et3h5nfhxxpziiwu
*is*related to*the*evaluation*of**the*Jones*and**Tutte*polynomials. ... We present an efficient quantum algorithm for*the*exact evaluation*of*either*the*fully ferromagnetic or anti-ferromagnetic q-state Potts*partition**function*Z for a family*of*graphs related to irreducible ... (9)*and**complexity*results concerning*the**Tutte*polynomial, that*the*evaluation*of**the*Potts*partition**function**is*also ♯P-hard. ...##
###
New graph polynomials from the Bethe approximation of the Ising partition function
[article]

2010
*
arXiv
*
pre-print

One

arXiv:0908.3850v2
fatcat:wfqimmothvdebdxxouqz4cwsrm
*is*a polynomial*of*two variables whose investigation*is*motivated by*the*performance analysis*of**the*Bethe*approximation**of**the**Ising**partition**function*. ... It*is*shown that these polynomials satisfy deletion-contraction relations*and*are new examples*of**the*V-*function*, which was introduced by*Tutte*(1947, Proc. Cambridge Philos. Soc. 43, 26-40). ... Acknowledgments This work was supported in part by Grant-in-Aid for JSPS Fellows 20-993*and*Grant-in-Aid for Scientific Research (C) 19500249. ...
« Previous

*Showing results 1 — 15 out of 1,427 results*