000063011 001__ 63011 000063011 005__ 20190709135510.0 000063011 0247_ $$2doi$$a10.1103/PhysRevE.96.032114 000063011 0248_ $$2sideral$$a101620 000063011 037__ $$aART-2017-101620 000063011 041__ $$aeng 000063011 100__ $$0(orcid)0000-0002-8215-1413$$aAzcoiti, Vicente$$uUniversidad de Zaragoza 000063011 245__ $$aAntiferromagnetic Ising model in an imaginary magnetic field 000063011 260__ $$c2017 000063011 5060_ $$aAccess copy available to the general public$$fUnrestricted 000063011 5203_ $$aWe study the two-dimensional antiferromagnetic Ising model with a purely imaginary magnetic field, which can be thought of as a toy model for the usual ¿ physics. Our motivation is to have a benchmark calculation in a system which suffers from a strong sign problem, so that our results can be used to test Monte Carlo methods developed to tackle such problems. We analyze here this model by means of analytical techniques, computing exactly the first eight cumulants of the expansion of the effective Hamiltonian in powers of the inverse temperature, and calculating physical observables for a large number of degrees of freedom with the help of standard multiprecision algorithms. We report accurate results for the free energy density, internal energy, standard and staggered magnetization, and the position and nature of the critical line, which confirm the mean-field qualitative picture, and which should be quantitatively reliable, at least in the high-temperature regime, including the entire critical line. 000063011 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E24-2$$9info:eu-repo/grantAgreement/ES/MINECO/FPA2012-35453$$9info:eu-repo/grantAgreement/ES/MINECO/FPA2015-65745-P 000063011 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000063011 590__ $$a2.284$$b2017 000063011 591__ $$aPHYSICS, MATHEMATICAL$$b7 / 55 = 0.127$$c2017$$dQ1$$eT1 000063011 591__ $$aPHYSICS, FLUIDS & PLASMAS$$b12 / 31 = 0.387$$c2017$$dQ2$$eT2 000063011 592__ $$a0.979$$b2017 000063011 593__ $$aCondensed Matter Physics$$c2017$$dQ1 000063011 593__ $$aStatistical and Nonlinear Physics$$c2017$$dQ1 000063011 593__ $$aStatistics and Probability$$c2017$$dQ2 000063011 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000063011 700__ $$aDi Carlo, Giuseppe 000063011 700__ $$0(orcid)0000-0002-4742-4279$$aFollana, Eduardo$$uUniversidad de Zaragoza 000063011 700__ $$0(orcid)0000-0003-1550-8168$$aRoyo-Amondarain, Eduardo$$uUniversidad de Zaragoza 000063011 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000063011 773__ $$g96, 3 (2017), 032114 [11 pp]$$pPhys. rev., E$$tPhysical Review E$$x2470-0045 000063011 8564_ $$s540414$$uhttps://zaguan.unizar.es/record/63011/files/texto_completo.pdf$$yVersión publicada 000063011 8564_ $$s131237$$uhttps://zaguan.unizar.es/record/63011/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000063011 909CO $$ooai:zaguan.unizar.es:63011$$particulos$$pdriver 000063011 951__ $$a2019-07-09-11:51:13 000063011 980__ $$aARTICLE