#-----------------------------------------------------------------------------
#                       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
#
#	
#
#		          Maple version
#                        ---------------
#
#       Read this file in Maple with:  > read"filename"; 
#
#
#
#______________________________
#Unfrustrated S=1/2 Spin Chain
#-----------------------------
#Linked cluster method:
#----------------------
#
#Susceptibility:
#
m[0] :=   1.:
m[1] :=  -4.:
m[2] :=   0.:
m[3] :=   64.:
m[4] :=   400.:
m[5] :=  -4032.:
m[6] :=  -89376.:
m[7] :=   163840.:
m[8] :=   26313984.:
m[9] :=   191334400.:
m[10] :=  -9565698560.:
m[11] :=  -210597986304.:
m[12] :=   3486950684672.:
m[13] :=   203634731188224.:
m[14] :=  -127324657152000.:
m[15] :=  -205019990184689664.:
m[16] :=  -3169755454477500416.:
m[17] :=   208763541109969256448.:
m[18] :=   8342101010835559022592.:
m[19] :=  -175912858271144581529600.:
m[20] :=  -18366266410738921187573760.:
m[21] :=  -40780317289246872850923520.:
m[22] :=   38668138493195891009425244160.:   
m[23] := 983734184997038611238624428032.:      
m[24] := -75650797544886562610211717119286.7:       
suceptibility_lc:=1/(4*T)*sum(m[i]/((i+1)!)*(J/(4*T))^i,i=0..24):
#
#Specific heat:
#
mc[2] := 6.0:
mc[3] := 36.:
mc[4] := -360.:
mc[5] := -7200.:
mc[6] := 15120.:
mc[7] := 1848672.:
mc[8] := 11426688.:
mc[9] := -594846720.:
mc[10] := -11558004480.:
mc[11] := 199812856320.:
mc[12] := 10106191180800.:
mc[13] := -19376365252608.:
mc[14] := -9289795522775040.:
mc[15] := -121944211136778240.:
mc[16] := 8791781390116945920.:
mc[17] := 310402124957945954304.:
mc[18] := -7225535925744106143744.:
mc[19] := -643407197363813620776960.:
mc[20] := 96147483542540314214400.:
mc[21] := 1279121513829538179364945920.:
mc[22] := 27962069861743501862336200704.:
mc[23] := -2398518627113966015427501883392.:
mc[24] := -129834725539335848980192847460554.112:
specific_heat_lc:=sum(mc[j]/(j!)*(J/(4*T))^j,j=2..24):
#
#
#Moment algorithm
#----------------
#
#Susceptibility:
#
suceptibility_ma:=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:
#
specific_heat_ma:= 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:
#
fsuceptibility_ma:=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:
#
fspecific_heat_ma:=(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):
#
# End of file