Qhov sib txawv tseem ceeb ntawm Ising thiab Heisenberg qauv yog tias nyob rau hauv tus qauv Ising, lub zog ntawm kev teeb tsa ntawm spin yog invariant nyob rau hauv flipping txhua spin nyob rau hauv lub system los ntawm mus rau los yog vice versa, whereas nyob rau hauv lub Heisenberg qauv, lub zog. ntawm ib tug configuration ntawm spin yog invariant mus thov tib yam kev sib hloov nyob ib ncig ntawm lub chav tsev sphere rau txhua tus kiv hauv lub system.
Ising qauv tau tsim thiab tau txais lub npe tom qab tus kws kho mob Ernst Ising. Tus qauv Heisenberg tau tsim los ntawm Werner Heisenberg, tus kws tshaj lij physicist.
Ising Model yog dab tsi?
Ising qauv yog tus qauv lej ntawm ferromagnetism hauv kev txheeb cais tshuab. Nws tau lub npe hu ua physicist Ernst Ising. Muaj qhov sib txawv tsis sib xws hauv cov qauv no sawv cev rau lub sijhawm sib nqus dipole ntawm atomic "spins" uas tuaj yeem tshwm sim hauv ib ntawm ob lub xeev, +1 thiab -1. Hauv cov qauv no, peb feem ntau npaj cov spin hauv ib lub lattice kom tso cai rau txhua qhov kev sib tw nrog nws cov neeg nyob ze. Cov qauv no tso cai rau peb txheeb xyuas cov theem hloov pauv raws li tus qauv yooj yim ntawm kev muaj tiag. Ising qauv yog ib qho ntawm cov qauv kev txheeb cais yooj yim tshaj plaws los qhia txog kev hloov pauv theem.
Thaum xav txog keeb kwm ntawm tus qauv no, nws tau tsim los ntawm physicist Wilhelm Lenz hauv xyoo 1920. Nws muab tus qauv no ua teeb meem rau nws cov tub ntxhais kawm; Ernst Ising nyob rau hauv 1925 qhov twg nws daws tus qauv. Tab sis nws txoj kev daws teeb meem tsis muaj kev hloov pauv hauv nws. Lub 2-dimensional square lattice Ising qauv yog ib qho nyuaj heev uas tau muab cov lus piav qhia los ntawm Lars Onsager hauv xyoo 1944. Feem ntau, cov qauv no tau daws los ntawm kev hloov-matrix txoj kev txawm tias muaj qee qhov sib txawv uas twb muaj lawm thiab. Thaum tus naj npawb ntawm qhov ntev yog siab tshaj plaub, qhov kev hloov pauv theem ntawm Ising qauv tuaj yeem piav qhia los ntawm "lub ntsiab lus teb txoj kev xav".
Heisenberg Model yog dab tsi?
Heisenberg qauv yog tus qauv lej hauv kev txheeb cais physics thiab tseem ceeb hauv kev kawm txog cov ntsiab lus tseem ceeb thiab theem hloov ntawm cov tshuab sib nqus. Nyob rau hauv cov qauv no, peb kho cov spin ntawm lub magnetic systems, quantum mechanically. Cov qauv no tau tsim los ntawm Werner Heisenberg, tus kws tshaj lij physicist. Cov qauv no muaj feem xyuam rau tus qauv Ising prototypical.
Daim duab 01: Heisenberg, W. thiab Wigner, E
Hauv quantum mechanics, qhov tseem ceeb ntawm kev sib txuas ntawm ob lub dipoles tuaj yeem ua rau cov neeg nyob ze tshaj plaws kom muaj lub zog qis tshaj thaum lawv ua raws. Ua qhov no ua qhov kev xav, peb tuaj yeem tsim cov qauv lej rau tus qauv Heisenberg.
Muaj qee qhov kev siv tseem ceeb ntawm tus qauv Heisenberg. Nws muab ib qho tseem ceeb thiab tractable theoretical piv txwv rau kev siv ceev matrix renormalization. Peb tuaj yeem daws cov qauv rau-vertex siv Heisenberg spin saw. Tsis tas li ntawd, tus qauv Hubbard ib nrab tuaj yeem ua rau ntawm tus qauv Heisenberg nrog kev sib txuas tsis tu ncua uas tsawg dua 0, sawv cev rau lub zog ntawm kev sib pauv pauv super.
Qhov txawv ntawm Ising thiab Heisenberg Model yog dab tsi?
Ising qauv thiab tus qauv Heisenberg tau tham feem ntau raws li kev txheeb xyuas lub cev. Qhov sib txawv tseem ceeb ntawm Ising thiab Heisenberg qauv yog tias nyob rau hauv tus qauv Ising, lub zog ntawm kev teeb tsa ntawm spin yog invariant nyob rau hauv flipping txhua spin nyob rau hauv lub system ntawm mus rau los yog vice versa whereas, nyob rau hauv lub Heisenberg qauv, lub zog ntawm ib tug configuration ntawm spin. yog invariant siv tib txoj kev sib hloov nyob ib ncig ntawm lub chav tsev sphere rau txhua tus kiv hauv lub system.
Hauv qab no yog cov ntsiab lus ntawm qhov sib txawv ntawm Ising thiab Heisenberg qauv hauv daim ntawv teev npe.
Summary – Ising vs Heisenberg Model
Ising qauv tau tsim thiab raug hu ua tus kws kho mob Ernst Ising thaum Heisenberg qauv tsim los ntawm Werner Heisenberg. Qhov sib txawv tseem ceeb ntawm Ising thiab Heisenberg qauv yog tias nyob rau hauv tus qauv Ising, lub zog ntawm kev teeb tsa ntawm spin yog invariant nyob rau hauv flipping txhua spin nyob rau hauv lub system ntawm mus rau los yog vice versa whereas, nyob rau hauv lub Heisenberg qauv, lub zog ntawm ib tug configuration ntawm spin. yog invariant siv tib txoj kev sib hloov nyob ib ncig ntawm chav tsev sphere mus rau txhua txhua spin nyob rau hauv lub system.
