(*---------------------------------------------------------------------------  *)
(*                       Coefficients of the HTSE                              *)
(*           for Unfrustrated and Frustrated S=1/2 Spin Chains                 *)
(*---------------------------------------------------------------------------  *)
(*               (cond-mat/0003221, to appear in EPJ B)                        *)
(**)
(*         Alexander Buehler, Norbert Elstner and Goetz S. Uhrig               *)
(**)
(*                      University of Cologne                                  *)
(*                Institute for Theoretical Physics                            *)
(*                           April 2000                                        *)
(**)
(**)
(**)
(*		          Mathematica version                                  *)
(*                        -------------------                                  *)
(**)
(*       Read this file in Mathematica with:  In[i] <<filename                 *)
(* *)
(* *)
(* *)
(*   ______________________________                                            *) 
(*   Unfrustrated S=1/2 Spin Chain                                             *)
(*   -----------------------------                                             *)
(*   Linked cluster method:                                                    *)
(*   ----------------------                                                    *)
(* *)
(*   Susceptibility:                                                           *)
(* *)
Array[m, 24]
m[0] =   1.0
m[1] =  -4.0
m[2] =   0.0
m[3] =   64.0
m[4] =   400.0
m[5] =  -4032.0
m[6] =  -89376.0
m[7] =   163840.0
m[8] =   26313984.
m[9] =   191334400.0
m[10] =  -9565698560.0
m[11] =  -210597986304.0
m[12] =   3486950684672.0
m[13] =   203634731188224.0
m[14] =  -127324657152000.0
m[15] =  -205019990184689664.0
m[16] =  -3169755454477500416.0
m[17] =   208763541109969256448.0
m[18] =   8342101010835559022592.0
m[19] =  -175912858271144581529600.0
m[20] =  -18366266410738921187573760.0
m[21] =  -40780317289246872850923520.0
m[22] =   38668138493195891009425244160.0   
m[23] = 983734184997038611238624428032.0      
m[24] = -75650797544886562610211717119286.7       
SuceptibilityLc[J_,T_]:=1/(4*T)*Sum[m[i]/((i+1)!)*(J/(4*T))^i,{i,0,24,1}]
(* *)
(*   Specific heat:                                                            *)
(* *)
Array[mc, 24]
mc[2] = 6.0
mc[3] = 36.0
mc[4] = -360.0
mc[5] = -7200.0
mc[6] = 15120.0
mc[7] = 1848672.0
mc[8] = 11426688.0
mc[9] = -594846720.0
mc[10] = -11558004480.0
mc[11] = 199812856320.0
mc[12] = 10106191180800.0
mc[13] = -19376365252608.0
mc[14] = -9289795522775040.0
mc[15] = -121944211136778240.0
mc[16] = 8791781390116945920.0
mc[17] = 310402124957945954304.0
mc[18] = -7225535925744106143744.0
mc[19] = -643407197363813620776960.0
mc[20] = 96147483542540314214400.0
mc[21] = 1279121513829538179364945920.0
mc[22] = 27962069861743501862336200704.0
mc[23] = -2398518627113966015427501883392.0
mc[24] = -129834725539335848980192847460554.112
SpecificHeatLc[J_,T_]:=Sum[mc[j]/(j!)*(J/(4*T))^j,{j,2,24,1}]
(* *)
(* *)
(*   Moment algorithm                                                          *)
(*   ----------------                                                          *)
(* *)
(*   Susceptibility:                                                           *)
(* *)
SuceptibilityMa[J_,T_]:=1/T*(1/4-1/8*J/T+1/96*J^3/(T^3)+5/1536*J^4/(T^4)-7/5120*J^5/(T^5)-133/122880*J^6/(T^6)+1/16128*J^7/(T^7)+1269/4587520*J^8/(T^8)+3737/74317824*J^9/(T^9)-339691/5945425920*J^10/(T^10)-1428209/54499737600*J^11/(T^11)+18710029/2242274918400*J^12/(T^12)+7045849/809710387200*J^13/(T^13)-358847/3957275492352*J^14/(T^14)-65174099663/28566582460416000*J^15/(T^15)-258645079463/498616712036352000*J^16/(T^16))
(* *)
(*   Specific heat:                                                            *)
(* *)
SpecificHeatMa[J_,T_] := 3/16*J^2/(T^2)+3/32*J^3/(T^3)-15/256*J^4/(T^4)-15/256*J^5/(T^5)+21/4096*J^6/(T^6)+917/40960*J^7/(T^7)+1417/327680*J^8/(T^8)-4303/688128*J^9/(T^9)-334433/110100480*J^10/(T^10)+37543/31457280*J^11/(T^11)+3987607/3170893824*J^12/(T^12)-1925339/41523609600*J^13/(T^13)-369233453/930128855040*J^14/(T^14)-31504270817/362750253465600*J^15/(T^15)+851758334701/8706006083174400*J^16/(T^16)
(* *)
(* *)
(* *)
(*   _____________________________                                              *)
(*   Frustrated S=1/2 Spin Chain                                               *)
(*   -----------------------------                                             *)
(*   Moment algorithm                                                          *)
(*   ----------------                                                          *)
(* *)
(*   Susceptibility:                                                           *)
(* *)
FSuceptibilityMa[J_,T_,alpha_]:=1/T*((15205963/5945425920*alpha^2-311903/82575360*alpha^3+9659/3932160*alpha^4-1177787/825753600*alpha^5+599639/594542592*alpha^6+791221/1486356480*alpha^7-367481/1486356480*alpha^8+22433/148635648*alpha^9-339691/5945425920*alpha^10-22843/1486356480*alpha-339691/5945425920)*J^10/(T^10)+(-34337/23592960*alpha+14125/4128768*alpha^2-1249/35389440*alpha^3+317/229376*alpha^4-969/655360*alpha^5+93463/61931520*alpha^6-67097/82575360*alpha^7-361/1720320*alpha^8+3737/74317824*alpha^9+3737/74317824)*J^9/(T^9)+(-23629/20643840*alpha-58651/13762560*alpha^2+28751/5160960*alpha^3-59/20160*alpha^4-877/1290240*alpha^5+5389/20643840*alpha^6-1271/1720320*alpha^7+1269/4587520*alpha^8+1269/4587520)*J^8/(T^8)+(5863/1474560*alpha-805/73728*alpha^2+3023/737280*alpha^3-381/81920*alpha^4+943/368640*alpha^5+67/368640*alpha^6+1/16128*alpha^7+1/16128)*J^7/(T^7)+(9/1280*alpha+221/61440*alpha^2-163/92160*alpha^3+7/15360*alpha^4+23/7680*alpha^5-133/122880*alpha^6-133/122880)*J^6/(T^6)+(-7/5120-49/6144*alpha+37/1536*alpha^2-1/128*alpha^3-7/5120*alpha^5+1/512*alpha^4)*J^5/(T^5)+(5/1536-23/768*alpha+1/512*alpha^2+5/1536*alpha^4-1/96*alpha^3)*J^4/(T^4)+(1/96+1/128*alpha+1/96*alpha^3-1/32*alpha^2)*J^3/(T^3)+1/8*J^2*alpha/(T^2)+(-1/8-1/8*alpha)*J/T+1/4)
(* *)
(*   Specific heat:                                                            *)
(* *)
FSpecificHeatMa[J_,T_,alpha_]:=(38993/1572864*alpha^8-334433/110100480*alpha^10-420475/11010048*alpha^2-334433/110100480+59305/2752512*alpha^3+92629/2752512*alpha+51701/1376256*alpha^5-1817/917504*alpha^7+27641/2752512*alpha^6-138811/2752512*alpha^4)*J^10/(T^10)+(2613/573440*alpha-4303/688128+5901/81920*alpha^5+1/10240*alpha^3-2229/573440*alpha^7-2411/143360*alpha^6-261/286720*alpha^4-4303/688128*alpha^9+3855/57344*alpha^2)*J^9/(T^9)+(35/2048*alpha^4-407/61440*alpha^5+2323/24576*alpha^2-59/960*alpha^3-2449/40960*alpha^6+1417/327680*alpha^8-4793/61440*alpha+1417/327680)*J^8/(T^8)+(-119/4096*alpha^2-245/8192*alpha^5+651/20480*alpha^4-2611/40960*alpha-413/4096*alpha^3+917/40960*alpha^7+917/40960)*J^7/(T^7)+(21/4096+105/1024*alpha^4+21/4096*alpha^6-363/4096*alpha^2+17/512*alpha^3+63/512*alpha)*J^6/(T^6)+(15/128*alpha^3-5/128*alpha^2-15/256*alpha^5-15/256+25/128*alpha)*J^5/(T^5)+(-3/32*alpha-15/256-3/32*alpha^2-15/256*alpha^4)*J^4/(T^4)+(-9/32*alpha+3/32*alpha^3+3/32)*J^3/(T^3)+(3/16*alpha^2+3/16)*J^2/(T^2)


Print["SuceptibilityLc=",SuceptibilityLc[J,T]]
Print["SpecificHeatLc=",SpecificHeatLc[J,T]]
Print["SuceptibilityMa=",SuceptibilityMa[J,T]]
Print["SpecificHeatMa=",SpecificHeatMa[J,T]]
Print["FSuceptibilityMa=",FSuceptibilityMa[J,T,alpha]]
Print["FSpecificHeatMa=",FSpecificHeatMa[J,T,alpha]]


(* *)
(* End of file *)