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ID:39123336
大小:1.30 MB
页数:44页
时间:2019-06-25
《复杂网络上Ashkin-Teller模型的相变》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、江西师范大学硕士学位论文复杂网络上Ashkin-Teller模型的相变姓名:欧阳坤申请学位级别:硕士专业:理论物理指导教师:乐建新20080601摘要在本文中,我们运用MonteCarlo方法研究了复杂网络上各向同性Ashkin—Teller模型的铁磁相变,其内容和结果包括以下两个方面:(1)利用MonteCarlo模拟,我们研究了一维附加型小世界网络上各向同性Ashkin-Teller模型的铁磁相变,得到了不同附加概率P下的三类相图。结果表明,各向同性Ashkin-Teller模型的三类相图都包含三个相,即完全有序的铁磁相(≠0,<盯>≠0,≠0,但----<盯>
2、)、完全无序的顺磁相(=0,<盯>=0,-0)以及部分有序的铁磁相(≠0,=0,<盯>-0)。当附加概率P较小时,各相之间的转变都是二级相变;而当附加概?率P增大时,在咒/K=1.0附近,完全有序的铁磁相和完全无序的顺磁相之间以及完全有序的铁磁相和部分有序的铁磁相之间的转变将逐渐出现一级相变。(2)利用MonteCarlo模拟,我们研究了二维重连型小世界网络上各向同性Ashkin-Teller模型的铁磁相变,并得到了不同重连概率P下的相图。结果表。一明,重连概率P对相图的结构影响很小,此类相图均由3个相组成,即完全有序的铁磁相(≠0,<盯>≠0,3、'S>≠0,但=<∥>)、完全无序的顺磁相(=0,=0,<盯J>_0)和部分有序的铁磁相(<盯s>≠0,=0,<仃>=0)。在x。/K=1.0附近,完全有序的铁磁相和完全无序的顺磁相之间以-及完全有序的铁磁相和部分有序的铁磁相之间的转变都出现了一级相变线,这与规则二维格子上各向同性Ashkin—Teller模型的铁磁相变有很大的不同。关键词:相变;复杂网络;MonteCarlo方法;相图AbstractInthisthesis,thephasetransitionsoftheisotropicAshkin.TellermodelOilthecomplexnetw4、orksarestudiedbyusingMonteCarlosimulations.Andthemainresultsareasfollows:.(1)WestudiedthephasetransitionsoftheisotropicAshkin.Tellermodelfortheferromagneticcaseonaone-dimensionaladding-typesmallworldnetwork,andgotthreevarietiesofphasediagramsfordifferentadditionalprobabilityP.Itisfound,thateachof5、thethreevarietiesofphasediagrams,fortheisotropicAshkin.Tellermodel,consistsofthreephases,i.e.,thefullyorderedferromagneticphase(≠0,<盯>≠0,≠0,but=<盯>),thefullydisorderedparamagneticphase(=0,<17">=0,<仃s>=O)andthepartiallyorderedferromagneticphase(≠0,=0,<盯>=0).Thereareonlysecond.6、orderphasetransitionsamongthreephasesinthephasediagramswithasmalleradditionalprobabilityP.。,...yHowever,withadditionalprobabilityPincreasing,first—orderphasetransitionsexistbetweenthefullyorderedferromagneticphaseandthefullydisorderedparamagneticphaseaswellasbetweenthefullyorderedferromagneticpha7、seandthepartiallyorderedferromagneticphaseinthephasediagramsclosetothestrengthK48、K!文.0.●‘~(2)WealsostudiedthephasetransitionsoftheisotropicAshkin.Tellermodelfortheferromagneticcaseonatwo—dimensionalrew。iring-typesmallw
3、'S>≠0,但=<∥>)、完全无序的顺磁相(=0,=0,<盯J>_0)和部分有序的铁磁相(<盯s>≠0,=0,<仃>=0)。在x。/K=1.0附近,完全有序的铁磁相和完全无序的顺磁相之间以-及完全有序的铁磁相和部分有序的铁磁相之间的转变都出现了一级相变线,这与规则二维格子上各向同性Ashkin—Teller模型的铁磁相变有很大的不同。关键词:相变;复杂网络;MonteCarlo方法;相图AbstractInthisthesis,thephasetransitionsoftheisotropicAshkin.TellermodelOilthecomplexnetw
4、orksarestudiedbyusingMonteCarlosimulations.Andthemainresultsareasfollows:.(1)WestudiedthephasetransitionsoftheisotropicAshkin.Tellermodelfortheferromagneticcaseonaone-dimensionaladding-typesmallworldnetwork,andgotthreevarietiesofphasediagramsfordifferentadditionalprobabilityP.Itisfound,thateachof
5、thethreevarietiesofphasediagrams,fortheisotropicAshkin.Tellermodel,consistsofthreephases,i.e.,thefullyorderedferromagneticphase(≠0,<盯>≠0,≠0,but=<盯>),thefullydisorderedparamagneticphase(=0,<17">=0,<仃s>=O)andthepartiallyorderedferromagneticphase(≠0,=0,<盯>=0).Thereareonlysecond.
6、orderphasetransitionsamongthreephasesinthephasediagramswithasmalleradditionalprobabilityP.。,...yHowever,withadditionalprobabilityPincreasing,first—orderphasetransitionsexistbetweenthefullyorderedferromagneticphaseandthefullydisorderedparamagneticphaseaswellasbetweenthefullyorderedferromagneticpha
7、seandthepartiallyorderedferromagneticphaseinthephasediagramsclosetothestrengthK4
8、K!文.0.●‘~(2)WealsostudiedthephasetransitionsoftheisotropicAshkin.Tellermodelfortheferromagneticcaseonatwo—dimensionalrew。iring-typesmallw
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