‡ ˜ m; c " e à à ŠŽ Ò Þ À W ¥ M X ê sT + b Ç \ Æ k Ó À W ¥ “ ¤” X ¢ä ì È ü Glauber Æ U ؎ Ò Þ] K ¡X ì Ä Ising { ¢¨ | ; c" e8 ý + s Ò “ Ö ¨ ” ôV ê s: à X Ø? _³ oz º  ¹ ō ˜ mS ó o Þ vs. Master U ê sX N ËÅ k Ä U ê s0 n É

S

‡ ˜ m; c   " e à à ŠŽ Ò Þ À W ¥  M X ê sT  + b Ç \ Æ k Ó À W ¥ “ ¤” X ¢ä ì È ü Glauber Æ U ؎ Ò Þ] K ¡X ì Ä Ising { ¢¨ | ; c" e8 ý + s Ò “ Ö ¨ ”  ôV ê s: à X Ø? _³  oz º  ¹ ō ˜ mS ó o Þ vs. Master U ê sX N ËÅ k Ä U ê s0 n É



¡) o £ Ó ^∗

Ø 

æ· ¡ ¤ @ /† < Ɠ § l œ íõ † < ƃ  ½ ¨™ è x 9  Ó ü t o † < Æõ , ' õ AÅ Ò 361-763 (2006¸   9 Z 4 15{ 9  ~ à Î6 £ §)

r

ç ß –\    " f ”  1 l x   H  l  © œs     9e ”   H Á ºô  Ç# 3 0 A Glauber î  r1 l x † < Æ — ¸4 S q`  ¦  Û ¼'  (Master)

~

½ Ó& ñ d ” Ü ¼– Ð ] X   H ô  Ç# Œ % 3 “ É r Tom´ e ü < de Oliveira_  ~ ½ Ó& ñ d ” õ   7 H _ …º ú ˜– Ð „  í ß –r Ð 3 x \ " f % 3 “ É r  l   6 £ § (magnetic hysteresis) / B G‚  `  ¦ q “ § % i  . Ä ºo   H s [ þ t   6 £ §/ B M‚  s  é ß –í  H ô  Ç r ç ß –_  F » ¡ ¤' ‘ \  _ K " f

› '

aº   t Ö  ¦ à º \ O 6 £ §`  ¦ µ 1 Ï|  % i  . Õ ªo “ ¦ ¿ º   6 £ § “ ¦‚    s _  t ƒ   ) a 0 A © œ  s [ þ t`  ¦ ƒ  › ' a t Ö  ¦ à º e ”

  H “ ¦o e ” s  S X ‰ “   % i  .

PACS numbers: 05.10.Ln, 05.50.+q, 05.70.Jk

Keywords:  7 H _ …º ú ˜– Ð „  í ß –r Ð 3 x, Glauber î  r1 l x † < Æ,   6 £ § ‰ & ³ © œ

I. " e  ] Ø

 

6 £ § (hysteresis)‰ & ³ © œ [1–3]“ É r  ƒ  > _  • ¸% ƒ\  ¼ # F ÷ &

#

Q e ”  . s  ‰ & ³ © œ“ É r # Œ Qt  B j m 7 £ § Ü ¼– Ð Â Ò'  Ò q tl   H X

<, : £ ¤ y  t è ß – # Œ Q K  1 l x î ß – r ç ß –\    " f ”  1 l x   H   l

 © œ_  % ò † ¾ Ó A  e ”   H Ó ü t o > \ " f { 9 # Q
  H 1 l x§ 4 † < Æ& h     6

£ § (dynamic hysteresis) s  @ /é ß –ô  Ç < É ª p \  ¦ = å J% 3   [4]. s  1

l x§ 4 † < Æ& h    6 £ §“ É r q ¨ î + þ A : Ÿ x > % i † < Æ\ " f s  : r& h Ü ¼– Ð ] X   H

l   © œ / 'î  r õ ] j– Ð · ú ˜ 94 R e ”  .

#

Œ Q ƒ  ½ ¨ [ þ t“ É r  “  † < Êà º
 F G ô  Ç& h Ü ¼– Ð a % v“ É r ` O Û ¼° ú  

“ É

r r ç ß –\    " f ”  1 l x   H  l  © œ_  & h 6   x \  _ K " f Ò q t l

  H 1 l x§ 4 † < Æ& h    6 £ § s 
 
  H Û ¼— 2 ; — ¸4 S q\  @ /K " f ƒ  

½

¨\  ¦ ô  Ç   e ”  . Û ¼— 2 ;>  ”  1 l x  l  © œ\  _ K " f 1 l x

| ¨

c M : > _  \ P % i † < Æ& h  ì ø Í6 £ x“ É r   # Qï  r ”  1 l x  l  © œ ˜ Ð  0 A



© œs  t ƒ  ÷ &  H  l  o (magnetization)_  ¢ - a  o ”  1 l x Ü ¼– Ð

×

¼ Qè ß – . s  Qô  Ç t ƒ   ) a ì ø Í6 £ x s  1 l x§ 4 † < Æ& h    6 £ § _  l " é ¶ s

 9  l  oü <  l  © œ_    6 £ § / B G‚  Ü ¼– Ð
 è ß – . s  Q ô

 Ç   6 £ § ‰ & ³ © œ_  ƒ  ½ ¨\   Û ¼'  (Master) ~ ½ Ó& ñ d ”  [5] ] X   H

~

½ ÓZ O `  ¦ s 6   x # Œ Tom´e ü < de Oliveira [6] % ƒ6 £ § Ü ¼– Ð s 



: r& h Ü ¼– Ð ƒ  ½ ¨ô  Ç ¨ î ç  H  © œ Û ¼— 2 ; — ¸4 S q`  ¦ ] jü @ “ ¦  H  7 H _ … º

ú

˜– Ð(MC) „  í ß –r Ð 3 x [7] s   ú ª“ É r # 3 0 A Û ¼— 2 ; — ¸4 S q\ " f_  1 l x

§

4 † < Æ& h    6 £ §`  ¦ ƒ  ½ ¨   H X < F  g# 3 0 A >  æ ¼# Œ”    e ”  .

Ä

ºo   H { 9 „  _  ƒ  ½ ¨ [8]\ " f, Á ºô  Ç # 3 0 A Glauber î  r1 l x

†

< Æ& h  Ising — ¸4 S q [9] [10] [11]`  ¦ : Ÿ x K " f MC „  í ß –r Ð 3 x _  r

ç ß –õ  ƒ  5 Å q& h “    Û ¼'  (Master) ~ ½ Ó& ñ d ” _  r ç ß – s _ 

∗

E-mail: [email protected]

› '

a > \  ¦ › ¸ ô  Ç   e ”  . Õ ª   õ  r ç ß –_  F » ¡ ¤' ‘  “   \  ¦ +

‹" f s [ þ t s  " f– Ð q Y V† < Ê`  ¦ ˜ Г    e ”  . s \  “ ¦Á º÷ &# Q Ä

ºo _  ƒ  ½ ¨\  ¦ r ç ß –\    " f ”  1 l x   H  l  © œs     2 ;

 â

Ä º\  S X ‰  © œ % i   H X <, Z  t ³ 1 Ñ> • ¸ MC „  í ß –r Ð 3 x Ü ¼– Ð % 3 “ É r

 

6 £ § / B G‚  õ   Û ¼'  ~ ½ Ó& ñ d ” `  ¦ s 6   x # Œ % 3 “ É r Tom´ e ü < de Oliveira [6] ~ ½ Ó& ñ d ” Ü ¼– Ð Â Ò'  % 3 “ É r   6 £ § / B G‚  s  F » ¡ ¤' ‘ 

 )

a r ç ß –ë ß –Ü ¼– Ð " f– Ð ƒ  › ' a ÷ &t  · ú §6 £ §`  ¦ µ 1 Ï|  % i  . s [ þ t s

 ƒ  õ ÷ &t  · ú §Ü ¼€   MC „  í ß –r Ð 3 x“ É r z  ´] jü <  Á º   › ' a

>

 \ O # Q4 R Ó ü t o & h  _ p \  ¦ { t  3 l w >  ÷ &# Q ë  H ] j  ) a



.

Õ

ªA " f ‘ : r ƒ  ½ ¨\ " f  H # Qb  G>  s [ þ t  l   6 £ § / B G‚  `  ¦

ƒ

 › ' a t Ö  ¦ à º e ”   H t \  @ /K " f / B N Â Ò l – Ð ô  Ç .

II. S ‡ ˜ m; c   " e à à ŠŽ Ò Þ À W ¥  M X ê s5 ; c" e8 ý

“

¤” X ¢ä ì È ü Æ U ؎ Ò Þ] K ¡X ì Ä Ising { ¢¨ | ; c å ¾ ˔ X ¢ Tom´ e Ñ ÷ de Oliveira8 ý  ­ Ž' [ U ê sX N ËÅ k ÄX ì Ä ± n É ¿ R <

r

ç ß –\    " f ”  1 l x   H  l  © œ? /\ " f_  Á ºô  Ç# 3 0 A Ising — ¸4 S q [12]“ É r  A _  Hamiltonian [6]Ü ¼– Ð & ñ _   ) a  .

H = − J 2N

N

X

i,j=1

s

i

s

j

− h(t)

N

X

i=1

s

i

. (1)

#

Œl " f s

ⁱ

  H ¶ ú ˜‚ ½ Ó(lattice)0 Au  i\ " f ±1° ú כ`  ¦ t   H Ising Û

¼— 2 ;   à º, J   H € ª œ(+)  Ҡ ñ_   À D K   ½ + Ë © œÃ º, N“ É r 8 ú x Û

¼— 2 ; > hà ºs “ ¦, r ç ß –\    " f ”  1 l x   H  l  © œ h(t) =

h

0

cos(ωt) \ " f h

0

  H  l  © œ ”  ; Ÿ ¤ Õ ªo “ ¦ ω   H y Œ • ”  1 l x à º

-381-

s

 . y Œ • ”  1 l x à º 0{ 9 M :, s  — ¸4 S q“ É r ¨ î + þ A © œI \ " f βJ = 1.0   © œ $ í \ " f y © œ $ í Ü ¼– Ð      H e ” > “ : r • ¸s  .

Ä

ºo   H s  — ¸4 S q_  — ¸Ž  H Û ¼— 2 ;s  ¢ - a„  y  & ñ § > =ô  Ç q ¨ î + þ A



© œI \ " f Ø  ¦ µ 1 Ï # Œ > _   l  o \ P & h  s  ¢ - a õ & ñ `  ¦   u

€  " f ˜ Ð# ŒÅ ҍ  H ”  1 l x‰ & ³ © œ`  ¦ › ¸  l – Ð ô  Ç . s  3 l q& h 

`

 ¦ 0 AK " f  H Tom´ e ü < de Oliveira [6]_  ~ ½ Ó& ñ d ” s  j þ t — ¸

e ”

 . Õ ª[ þ t“ É r  Û ¼'  ~ ½ Ó& ñ d ” õ   A _  Glauber „  s  S X ‰Ò  ¦ q

Ö  ¦

W (s

_i

→ −s

_i

) = 1

2τ

₀

[1 − s

_i

tanh(βE

_i

)], (2)

\

 ¦ s 6   x # Œ \ P % i † < Æ& h  F G ô  Ç\ " f  6 £ § õ  ° ú  “ É r q ¨ î + þ A   l

 o m(t) = P

N

i=1

< s

i

(t) > /N _  r ç ß –& h  ”   od ” `  ¦ Ä »

•

¸ % i  .

τ

₀

d

dt m(t) = −m(t) + tanh[β{J m(t) + h(t)}]. (3)

#

Œl " f τ

0

  H Glauber î  r1 l x † < Æ_  r ç ß –& h  ' ‘ • ¸\  ¦ [ O & ñ   H r

ç ß – é ß –0 A, E

i

= (J/N ) P

N

j=1

s

j

+ h(t), β = 1/k

B

T   H “ : r

•

¸_  % i à ºs  .

Ä

ºo   H ξ = ωt, K = βJ Õ ªo “ ¦ Ω = ωτ

⁰

° ú  “ É r " é ¶ s 

\ O

  H Ó ü t o | ¾ Ó`  ¦ + ‹" f 0 A_  ~ ½ Ó& ñ d ” `  ¦  6 £ § õ  ° ú  s  j þ t à º e ” 



.

Ω d

dξ m(ξ) = −m(ξ) + tanh[K{m(ξ) + h(ξ)

J }]. (4)

"

é

¶ g Ë :& h Ü ¼– Ð d ”  (5)  H  6 £ § õ  ° ú  “ É r + þ AI _  Û  ¦ s \  ¦ ”  



.

m(ξ) = P (ξ − φ), (5)

#

Œl " f P   H # Q‹ "  Å Òl † < Êà º\  ¦
 ? /“ ¦ φ   H ü @Â Ò ”  1 l x



l  © œ\ @ /ô  Ç  l  o_  t ƒ   ) a 0 A © œ`  ¦
  · p .

‘

: r ƒ  ½ ¨\ " f, < m(ξ) >\  › ' a ô  Ç d ”  (5)  H Runge-Kutta 4  Û  ¦ s \  ¦ + ‹" f à ºu & h Ü ¼– Ð Û  ¦% 3  . Á º " é ¶ _  r ç ß – ç ß –

 

 ξ  H 0.01 – Ð × þ ˜Ù þ ¡  H X <, & ñ S X ‰$ í õ  |   > í ß – r ç ß –é ß –> _ 

›

¸ o\  ¦ 0 AK " f s  . ² D G ™ è& h “   ¸ ú ˜2 £ § š ¸   H 10

⁻⁸

s ? /s 

“

¦, — ¸Ž  H r ç ß –\  @ / # Œ 4 o à º s  © œ_  à ºu  & ñ S X ‰$ í s  Ä

»t ÷ &• ¸2 Ÿ ¤ % i  .

III. S ‡ ˜ m; c   " e à à ŠŽ Ò Þ À W ¥  M X ê s5 ; 0" e8 ý

“

¤” X ¢ä ì È ü Æ U ؎ Ò Þ] K ¡X ì Ä Ising { ¢¨ | ; c å ¾ ˔ X ¢ MC

 ¹

ō ˜ mS ó o Þ ± n É ¿ R <

‘

: r ƒ  ½ ¨\ " f  H  Û ¼'  ~ ½ Ó& ñ d ” & h  ] X   H \   6   x ô  Ç Glauber î  r1 l x † < Æõ  { 9 › ' a$ í `  ¦ Ä »t  l  0 AK " f MC „  í ß –

r

Ð 3 x \  Glauber ! l rZ O (algorithm)`  ¦  6   x l – Ð ô  Ç . — ¸

Ž

 H Û ¼— 2 ;s  0 A– Ð & ñ § > =K  e ”   H œ íl  › ¸| Ü ¼– Ð Â Ò'  Ø  ¦ µ 1 Ï 

#

Œ ¶ ú ˜‚ ½ Ó 0 Au  i\  ¦ ‚  × þ ˜ô  Ç Ê ê τ

⁰

= 1 – Ð [ O & ñ “ ¦ d ”  (2)_ 

„

 s  S X ‰Ò  ¦ q Ö  ¦ W (s

i

→ −s

_i

)\  ¦ > í ß –ô  Ç .



6 £ § Ü ¼– Ð R ∈ (0, 1)“   è ß –Ã º\  ¦ µ 1 ÏÒ q tr v “ ¦, W (s

ⁱ

→

−s

i

) > R s €   s

_i

\  ¦ −s

i

– Ð  õ  H  . Õ ªX O t  · ú §“ É r  â Ä º\ 



 H D h– Ðî  r ¶ ú ˜‚ ½ Ó 0 Au \  ¦ ‚  × þ ˜ # Œ ° ú  “ É r õ & ñ `  ¦ N − 1  

÷

&Û  ¦ s  ô  Ç . Ä ºo   H s  כ `  ¦ Û ¼— 2 ;{ © œ 1 MC é ß –> (MCS/S)



“ ¦  ÒØ Ô 9, s  כ `  ¦ MC „  í ß –r Ð 3 x \ " f é ß –0 A r ç ß –Ü ¼– Ð



Œ

™  H  .

‘

: r ƒ  ½ ¨_  MC „  í ß –r Ð 3 x \ " f  H 200Z O _  œ íl  è ß –à º C 

\ P

`  ¦ G 6   x % i “ ¦, % ƒ6 £ § \   H > _  — ¸Ž  H Û ¼— 2 ;[ þ t s  0 A– Ð & ñ

§ >

= • ¸2 Ÿ ¤ % i  . 1 MCS/S   , < m(t) >\  ¦ l 2 Ÿ ¤ % i  Ü

¼ 9 s  õ & ñ “ É r 1,000   ì ø Í4 Ÿ ¤ % i  .

IV. Tom´ e Ñ ÷ de Oliveira8 ý  ­ Ž' [ U ê sX N ËÅ k ÄX ì Ä

± n

É ¿ R <Ê Ý MC  ¹ ō ˜ mS ó o Þ8 ý å ¾ Ë4 

· ú

¡‚   ƒ  ½ ¨ [8]\ " f Ä ºo   H MC „  í ß –r Ð 3 x _  r ç ß – t

M C

_  é

ß –0 A MCS/Sü < ƒ  5 Å q& h “    Û ¼'  ~ ½ Ó& ñ d ” _  r ç ß – t s  _

 › ' a > \  ¦ › ¸  % i  . 7 £ ¤, MC „  í ß –r Ð 3 x Ü ¼– Ð Â Ò'  % 3 

“ É

r  l  o  « Ñ\ " f  l  o ¨ î + þ A\  • ¸² ú ˜ l  f ” „   _

 ° ú כ\  K { © œ   H : £ ¤$ í r ç ß –`  ¦ ½ ¨ “ ¦, ° ú  “ É r  l  o ° ú כ

`

 ¦ t   H : £ ¤$ í r ç ß –`  ¦ Tom´ e ü < de Oliveira [6]_  ~ ½ Ó& ñ d ”

_  à ºu  Û  ¦ s \ " f ½ ¨ €   t

M C

= αt s  . # Œl " f α = α(βJ, h/J, N )“ É r : £ ¤$ í r ç ß –_  q \  ¦
  · p .

ô

 Ǽ # , MC „  í ß –r Ð 3 x \ " f_  y Œ •”  1 l x à º ω

^{M C}

  Û ¼' 

~

½ Ó& ñ d ”  ] X   H \ " f_  y Œ •”  1 l x à º ω\  q Y V Ù ¼– Ð ü @Â Ò  l 



© œ_  y Œ •”  1 l x à º  H & h ] X ô  Ç r ç ß – é ß –0 A\  ¦ l ï  r Ü ¼– Ð K $ 3 K 



 ô  Ç . 7 £ ¤, ω

M C

= ω/α s Ù ¼– Ð ξ = ωt = ω

^{M C}

t

M C

= ξ

_{M C}

s  . # Œl \ " f ξ

M C

  H MC „  í ß –r Ð 3 x _  Á º " é ¶ r  ç

ß –s  . Õ ªo  # Œ MC „  í ß –r Ð 3 x \ " f % 3 # Qt   H  l  o  H

m

M C

(ξ

M C

) = P

⁰

(ξ

M C

− φ

M C

), (6)

“

 X <,

m

_{M C}

(ξ) = P

⁰

(ξ − φ

_{M C}

), (7)

–

Ð ³ ð‰ & ³½ + É Ã º e ”  . # Œl " f P

⁰

“ É r # Q‹ "  Å Òl † < Êà ºs  9, φ

M C

  H Á º " é ¶  l  © œ h cos(ξ

M C

) = h cos(ξ) ? /\ " f_  t

ƒ   ) a 0 A © œ`  ¦ _ p ô  Ç . t ƒ   ) a 0 A © œ[ þ t“ É r φ

M C

6= φ s  Ù

¼– Ð, 0 A_  2t  ~ ½ ÓZ O `  ¦ + ‹" f % 3 “ É r   6 £ § / B G‚  [ þ t“ É r é ß –í  H

y

 F » ¡ ¤& h  ) a r ç ß – αt ë ß –`  ¦ s 6   x K " f  H ƒ  › ' a s  ÷ &t  · ú §  H



.

Õ

ªX O t ë ß – t ƒ   ) a 0 A © œ 

∆φ = φ − φ

_{M C}

, (8)

\

 ¦ + ‹" f d ”  (7)`  ¦

m

M C

(ξ) = P

⁰

(ξ − φ + ∆φ). (9) ü

< ° ú  s  ³ ð‰ & ³½ + É Ã º e ” Ü ¼ 9, Õ ªo  # Œ s [ þ t   6 £ § / B G‚  • ¸

"

f– Ð q “ §½ + É Ã º e ” >   ) a  . # Œl " f t ƒ   ) a 0 A © œ  ∆φ  H

¼

# _  © œ Tom´eü < de Oliveira ~ ½ Ó& ñ d ” _  à ºu  Û  ¦ s ü < MC

„

 í ß –r Ð 3 x Ü ¼– Ð Â Ò'  ½ ¨ô  Ç   6 £ §/ B G‚  \ " f  l  o þ j@ /u 

\

" f 0Ü ¼– Ð b  # Qt   H r ç ß –\  y Œ •”  1 l x à º\  ¦ Y  L ô  Ç ° ú כ_  s 

–

Ð & ñ _  l – Ð ô  Ç . Ó ü t : r   É r & ñ _ • ¸ 0 p x  .

V. Tom´ e Ñ ÷ de Oliveira U ê sX N ËÅ k Ä8 ý • ¤V  þ

s ÚT Ñ ÷ MC  ¹ ō ˜ mS ó o Þ + s ÇÊ Ý8 ý R w ‹

‘

: r ] X \ " f  H Tom´ e ü < de Oliveira ~ ½ Ó& ñ d ” _  à ºu  Û  ¦ s  ü

< MC „  í ß –r Ð 3 x   õ \  ¦ q “ § # Œ s [ þ t  s _  › ' a > \  ¦

½

©" î l – Ð ô  Ç . ½ ¨^ ‰& h Ü ¼– Ѝ  H, y Œ •”  1 l x à º  H  Œ •“ É r X < ü @ Â

Ò  l  © œ_  ”  ; Ÿ ¤ s  ß ¼€    l  o € ª œ(+)õ  6 £ §(-)  s _ 

Fig. 1. < m(ξ) > vs. h(ξ)/J for the infinite-range Glauber kinetic Ising model at βJ = 0.5 when the dimen- sioless magnetic field amplitude is h

0

/J = 1.0 and the angular frequency is ω = 0.001∗2π rad/s. Here, the solid circle, upside-down triangle and square symbols denote the MC simulation results for a lattice size N is equal to 1000, 10000, 100000, respectively. The solid line denotes the numerical solution of Tom´ e and de Oliveira differen- tial equation and the dashed line denotes the fitting of the numerical solution of Tom´ e and de Oliveira to MC results with the delayed phase difference ∆φ = 0.0095 rad

Fig. 2. < m(ξ) > vs. h(ξ)/J for the infinite-range Glauber kinetic Ising model at βJ = 1.0 when the dimen- sioless magnetic field amplitude is h

0

/J = 1.0 and the angular frequency is ω = 0.001∗2π rad/s. Here, the solid circle, upside-down triangle and square symbols denote the MC simulation results for a lattice size N is equal to 1000, 10000, 100000, respectively. The solid line denotes the numerical solution of Tom´ e and de Oliveira differen- tial equation and the dashed line denotes the fitting of the numerical solution of Tom´ e and de Oliveira to MC results with the delayed phase difference ∆φ = 0.0251 rad

Fig. 3. < m(ξ) > vs. h(ξ)/J for the infinite-range

Glauber kinetic Ising model at βJ = 2.0 when the dimen-

sioless magnetic field amplitude is h

0

/J = 1.0 and the

angular frequency is ω = 0.001∗2π rad/s. Here, the solid

circle, upside-down triangle and square symbols denote

the MC simulation results for a lattice size N is equal to

1000, 10000, 100000, respectively. The solid line denotes

the numerical solution of Tom´ e and de Oliveira differen-

tial equation and the dashed line denotes the fitting of

the numerical solution of Tom´ e and de Oliveira to MC

results with the delayed phase difference ∆φ = 0.0216

rad

ƒ

 5 Å q& h “   ° ú כ`  ¦ | 9  à º e ” >  ÷ &  H @ /g A   6 £ § (symmetric hysteresis) ë ß –`  ¦ “ ¦ 9 l – Ð ô  Ç . ‘ : r ƒ  ½ ¨\ " f  H  À Òl 

 B Ä º # Q 9î  r q @ /g A   6 £ § (asymmetric hysteresis)`  ¦ ]

jü @ l – Ð ô  Ç .

Fig. 1“ É r y Œ •”  1 l x à º ω = 0.001 ∗ 2π rad/s, Á º " é ¶ “ : r • ¸ _

 % i à º βJ = 0.5, Á º " é ¶  l  © œ ”  ; Ÿ ¤ h

0

/J = 1.0{ 9 M : Á

ºô  Ç# 3 0 A Glauber î  r1 l x † < Æ& h  Ising— ¸4 S q_   l    6 £ §/ B G‚  

`

 ¦
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(Springer, New York, 1991).

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98.

Hysteresis in the Infinite-Range Glauber Kinetic Ising Model in a Time-Dependent Oscillating Field: Monte Carlo Simulations vs. the

Master Equation Approach

Suhk Kun Oh

^∗

Basic Science Research Institute and Department of Physics, Chungbuk National University, Cheongju 361-763

(Received 15 September 2006)

Hysteresis curves obtained from both Monte Carlo simulations and from the master equation approach via the Tom´ e and de Oliveira equation for the infinite-range Glauber kinetic Ising model in the presence of time-dependent external oscillating magnetic fields are compared. We found that these hysteresis curves cannot be related by simply introducing the re-scaled time. The differ- ence between lagging phases for the hysteresis curves turns out to be another piece of information necessary to relate the hysteresis obtained in the two ways curves.

PACS numbers: 05.10.Ln, 05.50.+q, 05.70.Jk

Keywords: Monts Carlo Simulation, Glauber kinetics, Hysteresis

∗

E-mail: [email protected]