
bahulak kshetra siddhant

ack bahulak kshetra siddhant ack saankhyikiya kshetra siddhant haye joe ack tatasth yaa aaveshit bahulak pranali key saankhyikiya vyavhaar kaa varnan kartaa haye. ise vibhajan kaary koo isake maanak kaee-ayami abhinn pratinidhitva seey ack sahayak kshetra kaary parr ack karyatmak abhinn pratinidhitva mein swatantrata kii kann degree parr parivartit karke praapt kiya jaa sakata haye, yaa tou hubbard-stratonovic parivartan yaa delta-karyatmak parivartan kaa upayog karke. bahulak kshetra siddhanton parr adharit computer anukaran upayogi parinam dene key liye dikhaae gaye hain, udaaharan key liye bahulak samadhanon (byrley 2007, schmid 1998), bahulak pighalane (schmid 1998, matson 2002, frederickson 2002) aur thermoplastics (byrley 2006) kii sanrachanaon aur gunon kii ganana karane key liye.
canonical samooh.
canonical vibhajan kaary kaa kann pratinidhitva.
edward (edward 1965) dwara pesh kiye gaye lacheele polymers key maanak nirantarta model, formula _ 1 raikhik monodispers homepolymer seey baney samadhan koo motey-daane vaale polymer kii ack pranali key roop mein maanata haye, jisamen shrinkhalaon key saankhyikiya yantriki koo nirantar gossian thread model (byrley 2007) dwara varnit kiya jaataa haye aur vilaayak koo antarnihit roop seey dhyaan mein rakhaa jaataa haye. gausi dhaga model koo asatat gausi shrinkhala model kii nirantarta seema key roop mein dekhaa jaa sakata haye, jisamen polymer koo nirantar, raikhik roop seey lochdaar tantuon key roop mein varnit kiya jaataa haye. iss tarah kii pranali key vihit vibhajan kaary koo, ack vyutkram tapman sootra _ 2 parr rakhaa jaataa haye aur aayatan sootra _ 3 mein seemit kiya jaataa haye, jise iss prakaar vyakt kiya jaa sakata haye
jahan sootra _ 5 dwara diye gaye maadhya bull kii kshamata haye,
khandon key beach vilaayak-madhyasth gair-bandhan antahkriya kaa pratinidhitva karate hue, jabaki sootra _ 7 shrinkhalaon kii harmonic bandhan oorjaa kaa pratinidhitva kartaa haye. baad vaale oorjaa yogdan koo iss prakaar taiyar kiya jaa sakata haye -
jahan sootra _ 9 saankhyikiya khand kii lambai haye aur sootra _ 10 bahulak soochkaank haye.
kshetra-saiddhaantik parivartan.
vihit vibhajan falan key mool kshetra-saiddhaantik pratinidhitva koo praapt karane key liye, ack polymer pranali key khand ghanatva prachaalak koo nimnalikhit mein prastut kartaa haye
iss paribhasha kaa upayog karke, koee bhee ee. kyu. koo phir seey likh sakata haye. (2) key roop mein
isake baad, ack model koo hubbard-stratonovic parivartan yaa delta-karyatmak parivartan kaa upayog karke ack kshetra siddhant mein parivartit kartaa haye.
jahan sootra _ 14 ack karyatmak haye aur
sootra _ 15 delta haye 
dwara diyaa gayaa karyatmak
sootra key saath _ 17 kaa pratinidhitva kartaa haye 
sahayak kshetra kaary. yahaan humm dhyaan dete hain kii, ack forier shrinkhala mein kshetra kaary kaa vistaar karate hue, iska tatparya haye kii aavadhik seema sthitiyaan sabhi dishaaon mein lagu kii jaati hain aur sootra _ 18-vector supercell key parasparik jaali vactor koo nirdisht karate hain.
vihit vibhajan kaary kaa mool kshetra-saiddhaantik pratinidhitva.
ee. kyu. aiss. kaa upayog karna. (3), (4) aur (5), humm canonical vibhajan function koo ee. kyu. mein punah taiyar curr sakate hain. (1) kshetra-saiddhaantik pratinidhitva mein, joe
kahaan
gair-paraspar kriyasheel polymers key aadarsh gais key liye vibhajan kaary key roop mein vyakhya kii jaa sakati haye aur
lochdaar oorjaa key saath shoonya kshetra mein ack mukt bahulak kaa path abhinn haye
baad key sameekaran mein ack shrinkhala sootra key gair-vinyas kii aniyantrit trijya _ 23. isake alawa, eq mein. (6) ekal bahulak kaa vibhajan kaary, joe kshetra sootra _ 24 key adheen haye, dwara diyaa gayaa haye
bhavya canonical samooh.
bhavya vihit vibhajan kaary kaa mool kshetra-saiddhaantik pratinidhitva.
bhavya canonical vibhajan kaary koo praapt karane key liye, humm canonical vibhajan kaary key liye isake maanak thermodynamic sambandh kaa upayog karate hain, joe isake dwara diyaa gayaa haye
jahan sootra _ 27 rasayanik kshamata haye aur sootra _ 28 ee. kyu. dwara diyaa gayaa haye. (6). yog kaa pradarshan karate hue, yeh bhavya canonical vibhajan kaary kaa kshetra-saiddhaantik pratinidhitva pradaan kartaa haye,
kahaan
sootra _ 31 key saath bhavya canonical kriya haye jise paribhaashit kiya gayaa haye
ee. kyu. (8) aur nirantar
isake alawa, rasayanik kshamata seey sambandhit mapdand dwara diyaa jaataa haye
jahan sootra _ 34 ee. kyu. dwara pradaan kiya jaataa haye. (7).
kshetra kaa ausat anuman.
bahulak kshetra siddhanton key liye ack maanak sanniktan ranneeti maadhya kshetra (aim. aff.) sanniktan haye, jisamen ack shabd dwara kaarravaai mein kaee-shareer antahkriya shabd koo pratisthaapit karna shamil haye jahaan pranali key sabhi nikaay ack ausat prabhaavi kshetra key saath baatchit karate hain. yeh drishtikon kissy bhee bahu-shareer samasya koo ack prabhaavi ack-shareer samasya mein yeh maanate hue cumm curr detaa haye kii model key vibhajan kaary abhinn anga mein ack ekal kshetra vinyas kaa prabhutva haye. aim. aff. sanniktan key saath samasyaon koo hull karane kaa ack pramukh laabh, yaa isake sankhyaatmak karyanvayan koo aamtaur parr aatm-susangat kshetra siddhant (aiss. see. aff. tii.) key roop mein sandarbhit kiya jaataa haye, yeh haye kii yeh aksar apekshaakrit cumm computational laagat parr jatil kaee-shareer pranaliyon key gunon aur vyavhaar mein kuchh upayogi antardrishti pradaan kartaa haye. iss sanniktan ranneeti key safal anuprayog polymer aur jatil taral padarthon kii vibhinn pranaliyon key liye paae jaa sakate hain, jaise ee.jee. uchch aanvik vajan key dridhata seey alag kiye gaye block coppolymer, atyadhik kendrit tatasth bahulak samadhan yaa atyadhik kendrit block polyelectrolyte (pee. ee.) samadhan (aiss. aich. aim. dee. 1998, matson 2002, frederickson 2002). haalaanki, aise kaee mamle hain jinake liye aiss. see. aff. tii. galat yaa yahaan taka kii gunaatmak roop seey galat parinam pradaan kartaa haye (bee. aeye. yuu. aar. ell. 2006aeye). inmein dialute aur semidialute sandrata vyavasthaon mein tatasth bahulak yaa polyelectrolyte samadhan, unake crum-vikaar sankraman key paas block coppolymer, unake charan sankraman key paas bahulak mishran aadi shamil hain. aisee sthitiyon mein vibhajan kaary abhinn roop seey kshetra-saiddhaantik model koo paribhaashit karane mein poori tarah seey ack ekal aim. aff. vinyas kaa prabhutva naheen haye aur isase door kshetra vinyas mahatvapurna yogdan dey sakate hain, jisake liye anuman key aim. aff. star seey parey adhik parishkrit ganana takneekon key upayog kii aavashyakta hoti haye.
uchch crum sudhaar.
samasya kaa saamana karane kii ack sambhavana aim. aff. sanniktan key uchch-crum sudhaaron kii ganana karna haye. tsonchev aur anya. agrani (ack-loop) crum mein utaar-chadhaav sudhaaron sahit aisee ranneeti vikasit kii, jisase bhautik vigyaan mein naee antardrishti praapt karane kii anumati millie. 
seemit pee samadhan (tsonchev 1999). haalaanki, aisee sthitiyon mein jahaan aim. aff. sanniktan kharaab haye, vaanchhit sateekta praapt karane key liye kaee computational roop seey integral mein uchch-crum sudhaar kii maang karna aavashyak haye.
punarsanchayit karane kii takneek.
kshetra siddhanton mein honey vaale majboot utaar-chadhaav kii samasyaon seey nipatane key liye ack vaikalpik saiddhaantik upkaran 1940 key dashak key anta mein punarsanyaman kii avadharana dwara pradaan kiya gayaa haye, jise mool roop seey quantum kshetra siddhanton (qft 's) mein utpann honey vaale karyatmak samakalan kii ganana karane key liye taiyar kiya gayaa haye. kyu. aff. tii. kii ack maanak sanniktan ranneeti mein vikshobh siddhant kaa upayog karke yugman sthiraank mein ack shakti shrinkhala mein karyatmak samakalan kaa vistaar karna haye. durbhagya seey, aam taur parr adhikansh vistaar shabd anant hoe jaate hain, jisase aisee gananaaen avyavahaarik hoe jaati hain (shirkov 2001). kyu. aff. tii. seey anantataon koo hataane kaa ack tarika haye punarsanchayit (byrley 2007) kii avadharana kaa upayog karna. isamen mukhya roop seey yugman maapdandon key nange moolyon koo pratisthaapit karna shamil haye, jaise ee.jee. vidyut avesh yaa dravyamaan, punarnirmit yugman maapdandon dwara aur iss parivartan key tahat bhautik maatraon mein parivartan kii aavashyakta naheen haye, jisase vikshobh vistaar mein seemit sharton kii or jaataa haye. punarsanchayit karane kii prakriya kii ack saral bhautik tasveer ack shaastriya vidyut avesh, sootra _ 35 key udaaharan seey kheenchi jaa sakati haye, jise ack dhruviya madhyam mein daala jaataa haye, jaise kii ack electrolyte samadhan mein. madhyam key dhruvikaran key kaaran avesh seey doori sootra _ 36 parr, iska coolomb kshetra prabhaavi roop seey ack falan sootra _ 37, i parr nirbhar karega.ee. 1970 key dashak kii shuruat mein, nange vidyut avesh key bajaay prabhaavi (punarnaveenikaran) avesh, sootra _ 35.jee. willson ney saankhyikiya pranaliyon kii mahatvapurna ghatnaaon kii jaanch karane key liye, punaraadhunikta samooh (aar. jee.) siddhant kii aupchaariktaa koo vikasit karke punaraadhunikta avadhaaranaon kii shakti kaa beedaa uthaaya (willson 1971).
punarakraman samooh siddhant.
aar. jee. siddhant aar. jee. parivartanon kii ack shrinkhala kaa upayog kartaa haye, jisamen seey pratyek mein ack motey-anaaj charan key baad paimaane mein parivartan (willson 1974) hotaa haye. saankhyikiya-yaantrik samasyaon key mamle mein charanon koo vibhajan yog yaa abhinn mein swatantrata kii degree koo kramik roop seey samaapt karke aur punah praapt karke lagu kiya jaataa haye joe vicharadhin model koo paribhaashit kartaa haye. dee genes ney iss ranneeti kaa upayog charan sankraman key paas pheromagnetism key shoonya-ghatak shaastriya vector model key vyavhaar aur ack jaali parr anant lambai kii bahulak shrinkhala key ack swa-avahelana yaadrichhik chalane key beach ack saadrishya sthaapit karane key liye kiya, bahulak bahishkrit aayatan ghatakon (dee genes 1972) kii ganana karane key liye. iss avadharana koo kshetra-saiddhaantik karyatmak samakalan key liye anukoolit karane kaa tatparya ack vyavasthit tareeke seey adhyayan karna haye kii vibhajan kaary samakalan (willson 1974) seey swatantrata kii ack nishchit sankhya koo samaapt karate hue aur punarpraapt karate hue ack kshetra siddhant model kaise badalata haye.
hartry kaa punarnirdharan.
ack vaikalpik drishtikon koo "hartry approximation" yaa "self-consistant vann-loop approximation" (amit 1984) key roop mein jaanaa jaataa haye. yeh sootra _ 39-crum aim. aff. yogdan mein gausi utaar-chadhaav sudhaar kaa laabh uthaata haye, model maapdandon koo phir seey samanya banaane key liye aur mahatvapurna ekagrata shasanon mein ekagrata key utaar-chadhaav key pramukh lambai paimaane koo ack swa-susangat tareeke seey nikaalata haye.
tadpole kaa punarnirdharan.
ack aur haal key kaam mein efimov aur nogovitsyn ney dikhaaya kii "tadpole renormalisation" kii avadharana key aadhar parr kyu. aff. tii. seey utpann ack vaikalpik renormalisation takneek, shaastriya kaee-kann pranaliyon (efimov 1996) key saankhyikiya yantriki mein utpann honey vaale karyatmak samakalan kii ganana key liye ack bahut hii prabhaavi drishtikon hoe sakata haye. unhone pradarshit kiya kii shaastriya vibhajan falan samakalan mein mukhya yogdan nimn-crum key tadpole-prakaar key fenman aarekh dwara pradaan kiye jaate hain, joe kann aatm-antahkriya key kaaran alag-alag yogdan key liye jimmedaar hain. iss drishtikon mein kii gaee punarsanyojan prakriya ack avesh key aatm-paraspar kriya yogdan parr prabhaav daalati haye (jaise ee.jee. ack electron yaa ack aayan), joe usa avesh (byrley 2007) kii upasthiti key kaaran nirvaat mein prerit sthir dhruvikaran key parinamswarup hotaa haye. jaisa kii ack pahale key kaam (efimov 1991) mein efimov aur ganbold dwara pramaanit kiya gayaa haye, vibhajan kaary key mool kshetra-saiddhaantik pratinidhitva kii kaarravaai seey vichalan koo hataane key liye tadpole renormalisation kii prakriya koo bahut prabhaavi dhang seey niyojit kiya jaa sakata haye aur ack vaikalpik karyatmak abhinn pratinidhitva kii or leey jaataa haye, jise gausi samkaksh pratinidhitva (jarr) kahaa jaataa haye. unhone dikhaaya kii prakriya vishleshanatmak gadbadi ganana key liye mahatvapurna roop seey behtar abhisaran gunon key saath karyatmak samakalan pradaan karati haye. baad key karyon mein bayurle aur anya. tadpole renormalisation prakriya key aadhar parr prabhaavi cumm laagat vaale anuman vidhiyon kaa vikas kiya, joe prototypical polymer aur pee samadhanon (burl 2006aeye, burl 2006bee, burl 2007aeye) key liye upayogi parinam dete hain.
sankhyaatmak anukaran.
ack anya sambhavana monte carlo (mc) algorithm kaa upayog karna aur feeled-saiddhaantik sutrikaran mein poorna vibhajan function integral kaa namuna lena haye. parinami prakriya koo taba bahulak kshetra-saiddhaantik anukaran kahaa jaataa haye. haal key ack kaam mein, halanki, byrley ney pradarshit kiya kii tathaakathit sankhyaatmak sanket samasya (byrley 2002) key kaaran buniyaadi kshetra-saiddhaantik pratinidhitva key sanyojan mein mc namunakaran avyavahaarik haye. kathinaaee parinami vitaran kaary kii jatil aur dolankari prakriti seey sambandhit haye, joe vaanchhit ushmaagatiki aur sanrachanaatmak maatraon key samooh ausat key kharaab saankhyikiya abhisaran kaa kaaran banati haye. aise mamalon mein saankhyikiya abhisaran mein teji laane key liye vishesh vishleshanatmak aur sankhyaatmak takneekon kii aavashyakta hoti haye (byrley 2003, byrley 2003aeye, byrley 2004).
kshetra pratinidhitva kaa arth.
ganana key liye karyapranali koo anukool banaane key liye, byrley ney cotchy key abhinn pramey kaa upayog karke sajaatiya aim. aff. samadhan key madhyam seey vibhajan falan key abhinn key samroop koo sthanantarit karane kaa prastaav rakhaa, joe isake tathaakathit "maadhya-kshetra pratinidhitva" koo pradaan kartaa haye. iss ranneeti koo pahale bair aur anya logon dwara safaltapurvak niyojit kiya gayaa thaa. kshetra-saiddhaantik electronic sanrachana ganana (bayer 1998) mein. byrley yeh pradarshit curr sakata haye kii yeh takneek mc namuna prakriya (byrley 2002, byrley 2002aeye) mein samooh ausat key saankhyikiya abhisaran kaa ack mahatvapurna twaran pradaan karati haye.
gausi samkaksh pratinidhitva.
baad key karyon mein bayurle aur anya. (baurley 2002, baurley 2002aeye, baurley 2003aeye, baurley 2004) ney tadpole renormalisation kii avadharana koo lagu kiya, jisase vibhajan function integral key "gausi samkaksh pratinidhitva" kii or leey jaataa haye, joe bhavya canonical samooh mein unnat mc takneekon key sanyojan mein haye. way aashvast roop seey pradarshit curr sakate hain kii yeh ranneeti aage bhee kuchh aur pradaan karati haye 
vaanchhit samooh ausat (byrley 2002) key saankhyikiya abhisaran mein vriddhi.

