(*---------------------------------------------------------------------------  *)
(*                       Coefficients of the HTSE                              *)
(*           for the dimerised and frustrated S=1/2 chain                   *)
(*---------------------------------------------------------------------------  *)  
(*                  (Phys. Rev. B, Vol. 64, 024428 (2001))                  *)
(**)
(*         Alexander Buehler, Ute Loew and Goetz S. Uhrig                    *)
(**)
(**)
(**)
(*                      University of Cologne                                  *)
(*                Institute for Theoretical Physics                            *)
(*                           February 2001                                        *)
(**)
(**)
(**)
(*		          Mathematica version                                  *)
(*                        -------------------                                  *)
(**)
(*       Read this file in Mathematica with:  <<filename                     *)
(* *)
(* *)
(* *)


(* *)
(*    DIMERISED AND FRUSTRATED CHAIN *)
(* *)
Tchi[beta_,delta_,alpha_] := ((-339691/5945425920*alpha^10+22433/148635648*alpha^9+(-31027/99090432*delta^2-367481/1486356480)*alpha^8+(14941/99090432*delta^2+791221/1486356480)*alpha^7+(-816989/2972712960*delta^4-370969/212336640*delta^2+599639/594542592)*alpha^6+(153863/495452160*delta^4+52919/106168320*delta^2-1177787/825753600)*alpha^5+(102007/495452160*delta^6-128473/41287680*delta^4+3402433/1486356480*delta^2+9659/3932160)*alpha^4+(943507/743178240*delta^6-1311053/743178240*delta^4-1295087/743178240*delta^2-311903/82575360)*alpha^3+(1754671/5945425920*delta^8-33937/27525120*delta^6+2661047/2972712960*delta^4+515117/123863040*delta^2+15205963/5945425920)*alpha^2+(97039/70778880*delta^8-14683/9175040*delta^6-15173/7741440*delta^4-322247/247726080*delta^2-22843/1486356480)*alpha-4776949/29727129600*delta^10+1374211/1981808640*delta^8+145961/990904320*delta^6+195049/2972712960*delta^4-215221/5945425920*delta^2-339691/5945425920)*beta^10+(3737/74317824*alpha^9-361/1720320*alpha^8+(5233/9175040*delta^2-67097/82575360)*alpha^7+(-13529/20643840*delta^2+93463/61931520)*alpha^6+(69103/41287680*delta^4-1387/430080*delta^2-969/655360)*alpha^5+(12337/20643840*delta^4+4099/2949120*delta^2+317/229376)*alpha^4+(138421/82575360*delta^6-74989/27525120*delta^4-29209/9175040*delta^2-1249/35389440)*alpha^3+(22877/20643840*delta^6+699/458752*delta^4+79/458752*delta^2+14125/4128768)*alpha^2+(158933/165150720*delta^8-12323/6881280*delta^6-2423/1835008*delta^4-3899/1474560*delta^2-34337/23592960)*alpha+15607/13762560*delta^8+263/1474560*delta^6+481/1376256*delta^4+979/3440640*delta^2+3737/74317824)*beta^9+(1269/4587520*alpha^8-1271/1720320*alpha^7+(6095/4128768*delta^2+5389/20643840)*alpha^6+(-61/64512*delta^2-877/1290240)*alpha^5+(29/15360*delta^4+5119/2580480*delta^2-59/20160)*alpha^4+(-3947/5160960*delta^4+479/1290240*delta^2+28751/5160960)*alpha^3+(33017/41287680*delta^6+1061/393216*delta^4-4203/655360*delta^2-58651/13762560)*alpha^2+(-1927/983040*delta^6+76009/20643840*delta^4+36983/20643840*delta^2-23629/20643840)*alpha+9623/13762560*delta^8-10831/10321920*delta^6+1507/20643840*delta^4+89/229376*delta^2+1269/4587520)*beta^8+(1/16128*alpha^7+67/368640*alpha^6+(-199/368640*delta^2+943/368640)*alpha^5+(113/147456*delta^2-381/81920)*alpha^4+(-583/245760*delta^4+1009/122880*delta^2+3023/737280)*alpha^3+(-857/368640*delta^4-131/36864*delta^2-805/73728)*alpha^2+(-3167/1474560*delta^6+571/98304*delta^4+4289/491520*delta^2+5863/1474560)*alpha-307/92160*delta^6-11/9216*delta^4-59/92160*delta^2+1/16128)*beta^7+(-133/122880*alpha^6+23/7680*alpha^5+(-13/2560*delta^2+7/15360)*alpha^4+(97/30720*delta^2-163/92160)*alpha^3+(-117/20480*delta^4+49/30720*delta^2+221/61440)*alpha^2+(3/2560*delta^4+1/1536*delta^2+9/1280)*alpha-1129/368640*delta^6-21/40960*delta^4-83/40960*delta^2-133/122880)*beta^6+(-7/5120*alpha^5+1/512*alpha^4+(-1/384*delta^2-1/128)*alpha^3+(1/512*delta^2+37/1536)*alpha^2+(7/6144*delta^4-67/3072*delta^2-49/6144)*alpha+23/3072*delta^4+1/1536*delta^2-7/5120)*beta^5+(5/1536*alpha^4-1/96*alpha^3+(7/512*delta^2+1/512)*alpha^2+(-3/256*delta^2-23/768)*alpha+7/512*delta^4+7/768*delta^2+5/1536)*beta^4+(1/96*alpha^3-1/32*alpha^2+(3/128*delta^2+1/128)*alpha+1/96)*beta^3+(1/8*alpha-1/16*delta^2)*beta^2+(-1/8-1/8*alpha)*beta+1/4)

Heat[beta_,delta_,alpha_] := (-334433/110100480*alpha^10+(38993/1572864-324557/11010048*delta^2)*alpha^8+(-1817/917504-53813/2752512*delta^2)*alpha^7+(27641/2752512-9087/131072*delta^4+3069/57344*delta^2)*alpha^6+(-14075/688128*delta^2-83087/1376256*delta^4+51701/1376256)*alpha^5+(116115/1835008*delta^2+5375/688128*delta^4-138811/2752512-125561/1835008*delta^6)*alpha^4+(38011/393216*delta^2-297061/2752512*delta^4+59305/2752512-35787/917504*delta^6)*alpha^3+(-214825/3670016*delta^8+6235/393216*delta^2-276889/5505024*delta^4-420475/11010048+51407/917504*delta^6)*alpha^2+(-205055/2752512*delta^8+621/114688*delta^6+6463/172032*delta^2+92629/2752512-981/458752*delta^4)*alpha-431449/22020096*delta^8-249061/22020096*delta^2-133325/11010048*delta^4-33811/3670016*delta^6-334433/110100480+49649/36700160*delta^10)*beta^10+(-4303/688128*alpha^9+(-2229/573440-11103/573440*delta^2)*alpha^7+(-2411/143360-27/143360*delta^2)*alpha^6+(5901/81920-26673/286720*delta^2+537/81920*delta^4)*alpha^5+(-111/896*delta^2+21597/286720*delta^4-261/286720)*alpha^4+(1359/35840*delta^2-4311/71680*delta^4+1/10240+1131/35840*delta^6)*alpha^3+(-6261/286720*delta^2-7923/57344*delta^4+3855/57344+40137/286720*delta^6)*alpha^2+(14211/143360*delta^6-16347/573440*delta^8+2613/573440-5913/286720*delta^4-7821/143360*delta^2)*alpha-18369/1146880*delta^8-1401/286720*delta^2+3531/286720*delta^6-4303/688128+3177/573440*delta^4)*beta^9+(1417/327680*alpha^8+(-2449/40960+6943/122880*delta^2)*alpha^6+(-407/61440+2951/61440*delta^2)*alpha^5+(35/2048-259/2048*delta^2+1287/10240*delta^4)*alpha^4+(-41/1280*delta^2+571/3840*delta^4-59/960)*alpha^3+(-1347/40960*delta^2-1369/40960*delta^4+2323/24576+4679/40960*delta^6)*alpha^2+(1981/12288*delta^6-1999/20480*delta^2+59/4096*delta^4-4793/61440)*alpha-4997/983040*delta^8+2199/81920*delta^2+5803/163840*delta^4+1417/327680+11221/245760*delta^6)*beta^8+(917/40960*alpha^7+(-245/8192+3297/40960*delta^2)*alpha^5+(651/20480+637/20480*delta^2)*alpha^4+(-413/4096+1379/20480*delta^4+651/10240*delta^2)*alpha^3+(1491/10240*delta^2-819/20480*delta^4-119/4096)*alpha^2+(-2611/40960-2009/40960*delta^4+1281/40960*delta^2+3339/40960*delta^6)*alpha+1393/40960*delta^2+623/40960*delta^4+399/8192*delta^6+917/40960)*beta^7+(21/4096*alpha^6+(105/1024-69/1024*delta^2)*alpha^4+(17/512-45/512*delta^2)*alpha^3+(-363/4096-579/4096*delta^4+303/2048*delta^2)*alpha^2+(63/512-123/512*delta^4+15/128*delta^2)*alpha+21/4096+73/4096*delta^6-177/4096*delta^2-333/4096*delta^4)*beta^6+(-15/256*alpha^5+(15/128-25/128*delta^2)*alpha^3+(-5/128-15/128*delta^2)*alpha^2+(-25/128*delta^4+25/128)*alpha-35/256*delta^4-15/256-15/128*delta^2)*beta^5+(-15/256*alpha^4-3/32*alpha^2+(3/32*delta^2-3/32)*alpha-15/256+3/128*delta^2-15/256*delta^4)*beta^4+(3/32*alpha^3+(-9/32+9/32*delta^2)*alpha+3/32+9/32*delta^2)*beta^3+(3/16+3/16*delta^2+3/16*alpha^2)*beta^2


(* *)
(*    DIMERISED CHAIN *)
(* *)

Tchidim[beta_,delta_]:=(-182357607317269/745930601206382592000*delta^8+1116582102301823/4475583607238295552000+30860378761391/74593060120638259200*delta^6-169097404668739/10656151445805465600*delta^14+6285092004168191/497287067470921728000*delta^16-114706799537333/248643533735460864000*delta^10-90442750894411/74593060120638259200*delta^12+33268250832001/27124749134777548800*delta^2+301983779893/208944145996185600*delta^4-468309667465837/1032826986285760512000*delta^18)*beta^18+(344293742347/228532659683328000*delta^12+146506668199/685597979049984000*delta^2-535584743809/228532659683328000*delta^10-804378832603/228532659683328000*delta^6-134460640739/62327089004544000*delta^4+52097662147/7031774144102400*delta^16-1051886885537/342798989524992000*delta^8+1228965600979/2590036809744384000-22234161829843/685597979049984000*delta^14)*beta^17+(-381013820701/85699747381248000*delta^6-15175092143/3767021862912000*delta^2-6536122273267/2742391916199936000*delta^8-258645079463/498616712036352000-150602416817/3808877661388800*delta^14+176252096491/342798989524992000*delta^10-8706451935593/1371195958099968000*delta^4+32635888627387/1371195958099968000*delta^12+10785364513867/5484783832399872000*delta^16)*beta^16+(1134039913/173130802790400*delta^8-104930723893/3808877661388800*delta^14+373889611/357082280755200*delta^4+125245014907/1713994947624960*delta^12-49949749/11719623573504*delta^2+196672854197/34279898952499200*delta^6-65174099663/28566582460416000+86433646963/11426632984166400*delta^10)*beta^15+(-656281799/76947023462400*delta^14+361148659/35876398694400*delta^2+9492225643/466393183027200*delta^4-358847/3957275492352+7897101007/652950456238080*delta^8+378600476623/3264752281190400*delta^12+5394474767/296795661926400*delta^6-10743048697/652950456238080*delta^10)*beta^14+(7045849/809710387200+16757/19818086400*delta^6+9861031/653996851200*delta^4+2172449/21799895040*delta^12+2790083/118908518400*delta^2-56229473/3923981107200*delta^8-9467111/71345111040*delta^10)*beta^13+(18710029/2242274918400-35760853/2615987404800*delta^2-212653873/5231974809600*delta^8-161397977/523197480960*delta^10-50519537/1046394961920*delta^4+193615997/5231974809600*delta^12-18989863/356725555200*delta^6)*beta^12+(-1428209/54499737600-9539/27525120*delta^10+98731/707788800*delta^8-674059/7431782400*delta^4-56827/1238630400*delta^6-2683/29030400*delta^2)*beta^11+(145961/990904320*delta^6-4776949/29727129600*delta^10+195049/2972712960*delta^4+1374211/1981808640*delta^8-215221/5945425920*delta^2-339691/5945425920)*beta^10+(263/1474560*delta^6+481/1376256*delta^4+3737/74317824+979/3440640*delta^2+15607/13762560*delta^8)*beta^9+(1269/4587520-10831/10321920*delta^6+1507/20643840*delta^4+89/229376*delta^2+9623/13762560*delta^8)*beta^8+(-307/92160*delta^6-59/92160*delta^2+1/16128-11/9216*delta^4)*beta^7+(-83/40960*delta^2-21/40960*delta^4-133/122880-1129/368640*delta^6)*beta^6+(-7/5120+1/1536*delta^2+23/3072*delta^4)*beta^5+(7/512*delta^4+5/1536+7/768*delta^2)*beta^4+1/96*beta^3-1/16*beta^2*delta^2-1/8*beta+1/4


Heatdim[beta_,delta_] := (211128422793049/812560567762944000*delta^8+5145779287709/108341409035059200*delta^2+8816140320217/36934571261952000*delta^4+5854118848751/8291434364928000*delta^14+129505647760939/406280283881472000*delta^6-85986647698741/325024227105177600*delta^16+6827887220393/1329644565430272000*delta^18+19613319318773/90284507529216000*delta^10+88360795513999/406280283881472000*delta^12-80067486241427/4875363406577664000)*beta^18+(747694294049/114266329841664000*delta^8+501069785641/1904438830694400*delta^2+184265505341/3627502534656000+1750455145427/5193924083712000*delta^4+28645978566427/28566582460416000*delta^14+65018005163/453437816832000*delta^6-25549233744557/228532659683328000*delta^16-170193679963/5713316492083200*delta^10-221941384979/1269625887129600*delta^12)*beta^17+(-199750102373/307788093849600*delta^8+48804050567/692523211161600*delta^2-448010792927/1171962357350400*delta^4+718080430229/846417258086400*delta^14+851758334701/8706006083174400-577431395917/846417258086400*delta^6-1288308081349/60942042582220800*delta^16-141175079351/217650152079360*delta^10-6744074943121/5078503548518400*delta^12)*beta^16+(-3750596387/5580773130240*delta^8-7632645211/10364292956160*delta^2-31504270817/362750253465600-89314894561/72550050693120*delta^4+5917497137/14510010138624*delta^14-210219285347/217650152079360*delta^6-28368692533/51821464780800*delta^10-110329916941/43530030415872*delta^12)*beta^15+(-369233453/930128855040+2068244921/1993133260800*delta^8-967322681/1195879956480*delta^2+29175427/1993133260800*delta^4+3603293663/41855798476800*delta^14+5006543507/5979399782400*delta^6+1193462617/664377753600*delta^10-1410199439/543581798400*delta^12)*beta^14+(168008737/58133053440*delta^8-1925339/41523609600+60223033/39636172800*delta^2+2856603451/871995801600*delta^4+63260587/19818086400*delta^6+2484478763/435997900800*delta^10-140182523/96888422400*delta^12)*beta^13+(-238381/1056964608*delta^8+47342317/13212057600*delta^2+3987607/3170893824+70948027/26424115200*delta^4+16985329/19818086400*delta^6+2809583/377487360*delta^10-40555/117440512*delta^12)*beta^12+(-4199591/396361728*delta^8-2943281/1981808640*delta^2+37543/31457280-1231703/198180864*delta^4-2446939/330301440*delta^6+9792739/1981808640*delta^10)*beta^11+(-431449/22020096*delta^8-249061/22020096*delta^2-334433/110100480-133325/11010048*delta^4-33811/3670016*delta^6+49649/36700160*delta^10)*beta^10+(-18369/1146880*delta^8-1401/286720*delta^2-4303/688128+3177/573440*delta^4+3531/286720*delta^6)*beta^9+(-4997/983040*delta^8+2199/81920*delta^2+1417/327680+5803/163840*delta^4+11221/245760*delta^6)*beta^8+(1393/40960*delta^2+917/40960+623/40960*delta^4+399/8192*delta^6)*beta^7+(-177/4096*delta^2+21/4096-333/4096*delta^4+73/4096*delta^6)*beta^6+(-15/256-15/128*delta^2-35/256*delta^4)*beta^5+(-15/256+3/128*delta^2-15/256*delta^4)*beta^4+(3/32+9/32*delta^2)*beta^3+(3/16+3/16*delta^2)*beta^2


Print["Tchi=",Tchi[beta,delta,alpha]]
Print["Heat=",Heat[beta,delta,alpha]]


Print["Tchidim=",Tchidim[beta,delta]]
Print["Heatdim=",Heatdim[beta,delta]]

(* END OF FILE *)