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PHASE

TRANSITION

Nn0.

 PRENSENTING BY-

DIPENDRANATH MONDOLGITANJALI JANA

 JYOTSHNA DHILLON

NILANJAN BHAUMIK 

M.Sc PhysicsIIT Guwh!i

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In!"#$uc!i#n

• Phs% !"nsi!i#ns which #ccu" ! &%"# !%'(%"!u"%wh%n s#'% n#n-!h%"') ("'%!%" )i*% ("%ssu"%+ch%'ic) c#'(#si!i#n #" ',n%!ic %)$ is chn,%$"% c))%$ un!u' (hs% !"nsi!i#ns.

•  Th%y "% cus%$ /y un!u' uc!u!i#ns. 1%sh)) ,i2% n

in!"#$uc!i#n !# un!u' (hs% !"nsi!i#ns 3!%"c#))%c!in, 3%w /sic 3c!s /#u! (hs% !"nsi!i#nsn$ c"i!ic) /%h2i#u" w% $iscuss !h% i'(#"!nc% #3

un!u' '%chnics n$ !h% "%)!i#n /%!w%%nun!u' n$ c)ssic) !"nsi!i#ns s w%)) s !h%i"%4(%"i'%n!) "%)%2nc%.

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ase transition : From classical t 

antum Phase transition.•Phs% !"nsi!i#n is 2%"y c#''#n (h%n#'%n#n !# us..•M%)!in, #3 ic% ! 565K #" !h% !"nsi!i#n #3 i"#n 3"#' 3%""#',n%! !#("',n%! ! 660 "% !h% %4'()%s (hs% !"nsi!i#n .•Bu! 7s! #n% is (hs% !"nsi!i#n wi!h )!%n! h%! #" $isc#n!inui!y !!h% 7s! %n%",y $%"i2!i2% wi!h "%s(%c! !# T%'(%"!u"% /u! 5n$ #n% hs"s! $isc#n!inui!y ! 5n$ D%"i2!i2%. An$ w% c)ssi3y c)ssic) (hs%!"nsi!i#n !his wy.• E2%"y$y %4'()%s inc)u$% !h% M%)!#3 ic%+ '#"% c#'()ic!%$ is !h%!"nsi!i#n #3 '%!) in!# !h% su(%"c#n$uc!in, s!!% u(#n )#w%"in, !h%

!%'(%"!u"%. Th% uni2%"s% i!s%)3 is !h#u,h! !# h2% (ss%$ !h"#u,hs%2%") (hs% !"nsi!i#ns s !h% hi,h-!%'(%"!u"% ()s' 3#"'%$ /y!h% Bi, Bn, c##)%$ !# 3#"' !h% w#")$ s w% *n#w i! !#$y. Phs%!"nsi!i#ns #ccu" u(#n 2"i!i#n #3 n %4!%"n) c#n!"#) ("'%!%"8!h%i" c#''#n ch"c!%"is!ics is u)i!!i2% chn,% in !h% sys!%'("#(%"!i%s.•

  9un!u' (hs% !"nsi!i#ns h2% /%c#'% !#(ic #3 2i2i$ in!%"%s! in cu""%n! c#n$%ns%$ '!!%" (hysics. A! "s!

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As w% wi)) s%% /%)#w+ un!u' c"i!ic) /%h2i#"+ "isin, 3"#' !h%(%cu)i" %4ci!!i#n s(%c!"u' #3 !h% un!u' c"i!ic) ,"#un$

s!!%+ cn inu%nc% '%su"/)% un!i!i%s #2%" wi$% "n,% #3!h% (hs% $i,"'. Th% (hysic) ("#(%"!i%s #3 !h% un!u'uc!u!i#ns+ which cn $%s!"#y )#n,-"n,% #"$%" ! /s#)u!%&%"#+ "% ui!% $is!inc! 3"#' !h#s% #3 !h% !h%"') uc!u!i#ns"%s(#nsi/)% 3#" !"$i!i#n)+ ni!%-!%'(%"!u"% (hs% !"nsi!i#ns.

WHAT IS PHASE?

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BASIC PHENOMONA OF QUANTUM

PHASE TRANSITION

1% s!"! #u! wi!h /"i%y c#))%c!in, !h% /sic c#nc%(!s #3 (hs%!"nsi!i#ns n$ c"i!ic) /%h2i#u" which "% n%c%ss"y 3#" !h%)!%" $iscussi#ns. Phs% !"nsi!i#ns "% !"$i!i#n))y c)ssi%$ in!#"s!-#"$%" n$ c#n!inu#us !"nsi!i#ns. A! "s!-#"$%" !"nsi!i#ns !h%!w# (hs%s c#-%4is! ! !h% !"nsi!i#n !%'(%"!u"% : %4'()%s "%ic% n$ w!%" ! 0;

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1hi)% !h% !h%"'#$yn'ic 2%",% #3 !h% #"$%" ("'%!%" is &%"#in !h% $is#"$%"%$ (hs%+ i!s uc!u!i#ns "% n#n-&%"#. I3 !h% c"i!ic)(#in! is (("#ch%$+ !h% s(!i) c#""%)!i#ns #3 !h% #"$%"("'%!%" uc!u!i#ns /%c#'% )#n,-"n,%$.

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%4(#n%n!s : c#'()%!%)y ch"c!%"i&%s !h% c"i!ic) /%h2i#" n%" ("!icu)" (hs% !"nsi!i#n.

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 Quantum mechanics and the vicinity of

the critical point  Th% u%s!i#n #3 !# wh! %4!%n! un!u' '%chnics is i'(#"!n! 3#"un$%"s!n$in, c#n!inu#us (hs% !"nsi!i#n hs ! )%s! !w#s(%c!s. On !h% #n% hn$+ un!u' '%chnics cn /% %ss%n!i) !#un$%"s!n$ !h% %4is!%nc% #3 !h% #"$%"%$ (hs%+ =%.,.+

su(%"c#n$uc!i2i!y> : !his $%(%n$s #n !h% ("!icu)" !"nsi!i#nc#nsi$%"%$. On !h% #!h%" hn$+ #n% 'y s* wh%!h%" un!u''%chnics inu%nc%s !h% sy'(!#!ic c"i!ic) /%h2i#u". #" !his$iscussi#n w% h2% !# c#'("% !w# %n%",y sc)%s+ n'%)y Fhc+which is !h% !y(ic) %n%",y #3 )#n,-$is!nc% #"$%" ("'%!%"uc!u!i#ns+ n$ !h% !h%"') %n%",y *BT.

9un!u' '%chnics wi)) /% i'(#"!n! s )#n, s !his !y(ic) %n%",ysc)% is )",%" !hn !h% !h%"') %n%",y *BT8 #n !h% #!h%" hn$+ 3#"Fhc *BT (u"%)y c)ssic) $%sc"i(!i#n cn /% (()i%$ !# !h%#"$%" ("'%!%" uc!u!i#ns. In #!h%" w#"$s+ !h% ch"c!%" #3 !h%#"$%" ("'%!%" uc!u!i#ns c"#ss%s #2%" 3"#' un!u' !# c)ssic)

wh%n Fhc 3))s /%)#w *BT.

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s% "ns #ns nc"i!ic)

/%h2i#"• O"$%" P"'%!%" =7s! in!"#$uc%$ /y Ln$u>

• An #"$%" ("'%!%" is !h%"'#$yn'ic un!i!y !h! is &%"#in #n% (hs% =!h% $is#"$%"%$> n$ n#n-&%"# n$ n#n-uniu%in !h% #!h%" =!h% #"$%"%$> (hs%.

•  #" !h% 3%""#',n%!ic !"nsi!i#n+ !h% !#!) ',n%!i&!i#n is

n #"$%" ("'%!%"•  Th%"'#$yn'ic 2%",% #3 !h% #"$%" ("'%!%" is &%"# in

!h% $is#"$%"%$ (hs% /u! i!s uc!u!i#ns "% n#n-&%"#.

• As !h% c"i!ic) (#in! is(("#ch%$ !h% c#""%)!i#n !i'% $i2%",%s s

ν ξ  −=   || t 

ν 

ξ   −

=

  || t 

cτ 

cτ 

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9UANTUM ME

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N#w 3"#' En =5> !y(ic) !i'% sc)% τc  #3

!h% uc!u!i#ns $i2%",%s s c#n!inu#us!"nsi!i#n is (("#ch%$.