
kopra hastantaran matricks

sankhyikeey yantrikimadhye, kopra hastantaran matricks jaalimadhye chaturthansh jodanyachya parinamache varnan karato. rodney baxterne 1968 madhye crammers-vanier roow-too-roow transfer matrixcha vistar mhanoon sadar keela, tee jaali modelscha abhyas karanyachi eka shaktishali paddhat pradan karate. kopyatil hastantaran matricks kelelya gananene 1980 madhye baxterla katheen shatkon modelchya achook samadhanakade nele.
vyakhya.
aay. aar. eff. (parasparsanvad-goal-eka-chehara) model vicharat ghya, i.eae. pratyek sitela "i" niyukt kelelya σ "i" spins eka chauras jaali model aanee parasparsanvad samanya chehnyavaril firkiparyant maryadit aahe. ekoon urja yaa dware dilee jaau dya
jethe pratyek chehnyasathi sabhovatalachya thikananchi "i", "j", "k" aanee "l" khalilpramane mandani kelee aaheh
aine" sites asalelya jaalisathi, vibhajan karya aahe
jethe serve sambhavya firki sanrachananvar berries asate aanee 'doubleu' heey boltzmanche vajan asate.
sanketan sope karnyasathi, aapan pheromagnetic icing-prakarchi jaali vaparato jithe pratyek firkiche moolya + 1 kinwa-1 asate aanee jaminichi sthitee serve firkidware dilee jaate (i.eae. jevha jaalivaril serve firkiche moolya + 1 asate tevha ekoon urja qamee hote. aapan asehi gruheet dharato qee jaalimadhye 4 putt ghoornan samamiti (seema atinparyant) aahe aanee tee paravartan-avkal aahe. heey sulabh karnare gruhitak mahattvache naheet aanee sarvasadharan prakaranaparyant vyakhya vadhavane tulanene saral aahe.
aata khalee darshavilelya jaali chaturthanshacha vichar karah
trikonandware chinhankit bahya seema sthalanna tyanchi ground steet spin (yaa prakaranat + 1) niyukt kelee jaatat. khulya vartulanni chinhankit kelelya jaaga chaturthanshchya aateel seema tayar karatat; tyanchya sambandhit firki sanchanna {σ1. asey label dile jaate.., σ "m"} aanee {σ '1.., σ 'm'}, jethe σ1 = σ '1. pratyek aateel simesathi 2' m 'sambhavya sanrachana aahet, mhanoon aapan 2' m '× 2' m 'matrixchi praveshanihay vyakhya karato
matricks "aaa", tarr, dilelya jaali chaturthanshasathi koppyache hastantaran matricks aahe. bahya seema firki nishchit asalyane aanee serve aateel firkivar berries asalyane, "aaa" chee pratyek nond hii aateel seema firkiche karya aahe. abhivyaktitil kronekar delta heey sunishchit karate qee σ1 = σ '1, mhanoon sanrachananna yogya prakare krambaddha karoon aapan' a 'laa block vikarn matricks mhanoon takoo shakatoh
corner transfer matricks heey sopya paddhatine vibhajan karyashi sambandhit aahet. aamchya sopya udaharanat, aapan jaali chaturthanshchya chaar firavalelya pratinpasoon purn jaali tayar karato, jithe σ, σ ', σ' aanee σ 'chya aateel seema firki sanchanna bhinn honyachi parvanagi aaheh
vibhajan karya nantar kopyatil hastantaran matricks "aaa" chya sandarbhat asey lihile jaate
charcha.
punaravrutti sambandh.
kopyatil hastantaran matricks "a" 2 "m" ("m" × "m" chaturthanshasathi paribhashit) lahan kopyatil hastantaran matricks "a" 2 "m"-1 aanee "a" 2 "m"-2 (qamee ("m"-1) × ("m"-1) aanee ("m"-2) × ("m"-2) chaturthansh anukrame) chya sandarbhat vyakt keela jaau shakato. haah punaravrutti sambandh, tattvatah, maryadit aakarachya konatyahi jaali chaturthanshasathi kopyachya hastantaran matrixchi punaravrutti ganana karnyas anumati deto.
tyanchya rang-teey-rang samakakshanpramanech, kopyatil hastantaran matricks faces transfer matrixmadhye ghatak kele jaau shakatat, jeey jaalila ekach chehara jodanyashi sambandhit aahet. aadhi dilelya jaali chaturthanshasathi, faces transfer matricks aakar 2 'mea' × 2 'mea' chey asatat aanee praveshanihay paribhashit kele jaatat
jethe 2 ≤ "i" ≤ "m" + 1. bahya simejaval, visheshtah, aamchyakade aahe
tyamule kopyatil hastantaran matricks "aaa" haah ghatak mhanoon ghatak hoto
kuthe?
chitratmakdrushtya, heey yachyashi sambandhit aaheh
aaplyala 2 'm' × 2 'm' matricks 'a' * aanee 'a' * * chee dekhil aavashyakta aahe, jyadvare pravesh-vaar paribhashit kelya aahet
jethe 'aaa' matricks jyachya nondi rhs varr disatat tyaa anukrame 2 'm'-1 × 2 'm'-1 aanee 2 'm'-2 × 2 'm'-2 aakarachya asatat. heey adhik spashtapane asey lihile aahe qee
aata 'aaa', 'aaa', 'aaa', 'aaa', 'yuu', 'aay' aanee 'eff', jeey 'yaa vyakhyanmadhun, aaplyala
jeey "a" 2 "m"-1 aanee "a" 2 "m"-2 chya sandarbhat "a" 2 "m" sathee punaravrutti sambandh dete.
karnaroop.
ganana karnyasathi koppyache hastantaran matricks vapartana, tyaeivaji tyanchya karnarupansah kaam karane vishleshanatmak aanee sankhyatmakdrushtya donhi prakare soyiche aahe. heey sulabh karnyasathi, punaravrutti sambandh thet karnarupanchya aanee "aaa", "aaa", * aanee "aaa", * * chya eigenwector matrixchya sandarbhat punarlikhit keela jaau shakato.
aaplya udaharanatil jaali hii pratibimbit-bhinn aahe, yaa arthane lakshat gheta qee
aapan pahato qee "aaa" haah eka samamiteey matricks aahe (i.eae. orthogonal matrixdware teey tiryak kele jaau shakate). mhanoon aamhi lihito
jethe "a" "d" haah eka karn matricks aahe (samanyikrut assa qee tyachi sankhyatmakdrushtya sarvat mothee nond 1 aahe), "α" "m" heey "a" chey sarvat mothe aaygan moolya aahe aanee "p" "t" "p" = "i". tyachpramane 'aaa' * aanee 'aaa' * * sathee, aamchyakade aahe
jethe "a" "d" *, "a" "d" * *, "p" * aanee "p" * * hii "a" * aanee "a" * *, i "shhee samaan paddhatine paribhashit kelee jaatat.eae. a" 2 "m"-1 aanee "a" 2 "m"-2 chya lahan (samanyikrut) karnarupanchya aanee (orthogonal) eigenwector matrixchya sandarbhat.
yaa tiryakta punha punha honanya sambandhat badaloon, aapan midvato
kuthe?
aata "a" "t" dekhil samamiteey aahe aanee jarr "a" "d" * ", a" "d" * * aanee "r" * dnyat asateel tarr ganana kelee jaau shakate; "a" "t" vikarn kelyane tyache samanyikrut vikarn swaroop "a" "d", tyache sarvat mothe aaygan moolya "κ" aanee tyache orthogonal igenwector matricks "r" milate.
anuprayog.
firki apekshit moolya.
jaalichya aat kholvar asalelya vishisht thikani firkichya apekshit mulyasarkhya pramananchi ganana karnyasathi kopyatil hastantaran matricks (kinwa tyanche karnaroop) vaparale jaau shakatat. aadhi dilelya purn jaalisathi, madhyavarti thikanavaril firkichi apeksha moolya khalilpramane dilee jaateh
purvipramanech 'aaa' haah khand karn asel asha kramane kelelya sanrachanansah, aapan 2 'mea' × 2 'mea' karn matricks paribhashit karoo shakato.
asha prakare
prati sanketsthal vibhajan karya.
jaalichya pratikrutisathi aanakhi eka mahattvache praman mhanje prati sthal vibhajan karya, jyache thermodynamic maryadet moolyankan kele jaate aanee asey lihile jaate
aamchya udaharanat, heey qamee hote
kaaran 'm' = 'd' 4 hii 'm' = 'φ' mhanoon abhisari berries aahe aanee 'a' d 'haah anant-aayami hoto. yavyatirikt, 2 'm' ('m' + 1) chey chehare thermodynamic maryadet 'n' chya siteschya sankhyeparyant pohochatat, mhanoon aamchyakade aahe
jeey aadhichya samikaranashi susangat aahe, jeey "a" t "sathee sarvat mothe aaygan moolya mhanoon" κ "dete. dusya shabdant, prati site vibhajan karya thermodynamic maryadet kopyatil hastantaran matrixsathi karnabaddh punaravrutti sambandhadvare nemke dile jaate; yamule mothya jaalisathi "a" d "mojanyachya punaravrutti prakriyedvare" κ "andaje kele jaau shakate.
tathapi, tyat samavisht matricks aakarane vegane vadhatat aanee vastavik sankhyatmak gananet teey pratyek tappyavar kapale jaane aavashyak aahe. heey karnyacha eka marg mhanje kahee nishchit 'aine' sathee pratyek tappyavar 'aine' sarvat mothee eigenvalue thevane. bahutansh prakarananmadhye, "n" = 1,2,3 gheuun midavalelya andajancha kram.. jalad aanee achook mulyaparyant (achookpane sodavata yenyajogya pratimanasathi) ekatra yete.