资源描述：
《An Introduction to the Ising Model ocr.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、AnIntroductiontotheIsingModelBARRYA.CIPRA,St.OlafCollege,Northfield,Minnesota55057BarryCiprareceivedaPh.D.inmathematicsfromtheUniversityofMarylandin1980.HehasbeenaninstructoratM.I.T.andattheOhioStateUniversity,andiscurrentlyanassistantprofessorofmathematicsatSt.OlafColle
2、geinNorthfield,Minnesota.HeistheauthorofMisteaksandHowtoFindThemBeforetheTeacherDoes,publishedbyBirkhauserBoston.IntroductionThisarticleisaninvitation,oradvertisement,forreaderstoworkonaproblemwhichisapparentlyverydifficult,yetcertainlyextremelyimportant.Theproblemisknow
3、ngenericallyastheIsingmodel,namedafterErnstIsing,whodidthefirstworkonitintheearly1920s.Althoughunpromisinginitsinitialresults,theIsingmodelhasturnedouttobeanexceptionallyrichidea.Thenumberofpaperswrittenonthesubjectisstaggering;thenumberwhichremaintobewrittenisconceivabl
4、yevenmorestaggering.TheIsingmodelisconcernedwiththephysicsofphasetransitions,whichoccurwhenasmallchangeinaparametersuchastemperatureorpressurecausesalarge-scale,qualitati~echangeinthestateofasystem.Phasetransitionsarecommoninphysicsandfamiliarineverydaylife:weseeone,fori
5、nstance,wheneverthetemperaturedropsbelow320F,andanotherwheneverweputakettleofwateronthestove.Otherexamplesincludetheformationofbinaryalloysandthephenomenonofferromagnetism.Thelatterisalsoofinteresthistorically:anunderstandingofferromagnetism-andespecially"spontaneousmagn
6、etization"•wastheoriginalpurposeoftheIsingmodelandthesubjectofIsing'sdoctoraldissertation.Partlyforthishistoricalsignificance,weshalluseferromagnetismasareferencepointlateronforinterpretingvariousfeaturesofthemodel.Inspiteoftheirfamiliarity,phasetransitionsarenotwellunde
7、rstood.OnepurposeoftheIsingmodelistoexplainhowshort-rangeinteractionsbetween,say,moleculesinacrystalgiverisetolong-range,correlativebehavior,andtopredictinsomesensethepotentialforaphasetransition.TheIsingmodelhasalsobeenappliedtoproblemsinchemistry,molecularbiology,andot
8、herareaswhere"coop•erative"behavioroflargesystemsisstudied.TheseapplicationsarepossiblebecausetheIsingm
