Linear Perturbation Renormalization Group method for Ising-like spin systems
The linear perturbation group transformation (LPRG) is used to study the thermodynamics of the axial next-nearest-neighbor Ising model with four spin interactions (extended ANNNI) in a field. The LPRG for weakly interacting Ising chains is presented. The method is used to study finite field para-fer...
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| Дата: | 2013 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут фізики конденсованих систем НАН України
2013
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/121079 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Linear Perturbation Renormalization Group method for Ising-like spin systems / J. Sznajd // Condensed Matter Physics. — 2013. — Т. 16, № 1. — С. 13704:1–8. — Бібліогр.: 21 назв. — англ. |
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irk-123456789-1210792017-06-14T03:02:55Z Linear Perturbation Renormalization Group method for Ising-like spin systems Sznajd, J. The linear perturbation group transformation (LPRG) is used to study the thermodynamics of the axial next-nearest-neighbor Ising model with four spin interactions (extended ANNNI) in a field. The LPRG for weakly interacting Ising chains is presented. The method is used to study finite field para-ferrimagnetic phase transitions observed in layered uranium compounds, UAs₁-xSex, UPd₂Si₂ or UNi₂Si₂. The above-mentioned systems are made of ferromagnetic layers and the spins from the nearest-neighbor and next-nearest-neighbor layers are coupled by the antiferromagnetic interactions J₁<0 and J₂<0, respectively. Each of these systems exhibits a triple point in which two ordered phases (ferrimagnetic and incommensurate) meet the paramagnetic one, and all undergo the high field phase transition from para- to ferrimagnetic (++-) phase. However, if in UAs₁-xSex the para-ferri phase transition is of the first order as expected from the symmetry reason, in UT₂Si₂ (T=Pd, Ni) this transition seems to be a continuous one, at least in the vicinity of the multicritical point. Within the MFA, the critical character of the finite field para-ferrimagnetic transition at least at one isolated point can be described by the ANNNI model supplemented by an additional, e.g., four-spin interaction. However, in LPRG approximation for the ratio κ = J₂/J₁ around 0.5 there is a critical value of the field for which an isolated critical point also exists in the original ANNNI model. The positive four-spin interaction shifts the critical point towards higher fields and changes the shape of the specific heat curve. In the latter case for the fields small enough, the specific heat exhibits two-peak structure in the paramagnetic phase. Лiнiйне пертурбативне перетворення (LPRG) використовується для вивчення термодинамiки аксiальної моделi Iзинга з наступними до найближчих сусiдами з чотириспiновою взаємодiєю (розширена модель ANNNI) у полi. Представлено LPRG для слабовзаємодiючих ланцюжкiв Iзинга. Метод застосовано до ви-вчення пара-феромагнiтних фазових переходiв у скiнченному полi, що спостерiгаються в шаруватих спо-луках урану UAs₁−xSex, UPd₂Si₂ чи UNi₂Si₂. Вище згаданi системи зробленi з феромагнiтних шарiв i спi-ни з найближчих i наступних до найближчих шарiв є зв’язанi антиферомагнiтними взаємодiями J₁ < 0 i J₂ < 0, вiдповiдно. Кожна з цих систем демонструє потрiйну точку, в якiй двi впорядкованi фази (фе-ромагнiтна i неспiвмiрна) зустрiчаються з парамагнiтною фазою i всi фази зазнають фазового переходу у сильному полi з пара- до феромагнiтної (+ + −) фази. Проте, якщо в UAs₁−xSex є пара-феро фазовий перехiд першого роду, як очiкується з симетрiйних мiркувань, в UT₂Si₂ (T = Pd, Ni) цей перехiд видається неперервним, принаймнi в околi мультикритичної точки. В рамках наближення середнього поля, критич-ний характер пара-феромагнiтного переходу в скiнченному полi, принаймнi в однiй iзольованiй точцi, може бути описаний за допомогою моделi ANNNI, яка доповнена додатковою, наприклад, чотириспiно-вою взаємодiєю. Проте, в наближеннi LPRG для коефiцiєнта κ = J₂/J₁ поблизу 0.5 є критичне значення поля, для якого iзольована критична точка також iснує в оригiнальнiй моделi ANNNI. Позитивна чотири-спiнова взаємодiя зсуває критичну точку до вищих полiв i змiнює форму кривої питомої теплоємностi. В останньому випадку для достатньо малих полiв питома теплоємнiсть демонструє двопiкову структуру в парамагнiтнiй фазi. 2013 Article Linear Perturbation Renormalization Group method for Ising-like spin systems / J. Sznajd // Condensed Matter Physics. — 2013. — Т. 16, № 1. — С. 13704:1–8. — Бібліогр.: 21 назв. — англ. 1607-324X PACS: 75.10.Hk, 75.40.Cx DOI:10.5488/CMP.16.13704 arXiv:1303.5585 http://dspace.nbuv.gov.ua/handle/123456789/121079 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The linear perturbation group transformation (LPRG) is used to study the thermodynamics of the axial next-nearest-neighbor Ising model with four spin interactions (extended ANNNI) in a field. The LPRG for weakly interacting Ising chains is presented. The method is used to study finite field para-ferrimagnetic phase transitions observed in layered uranium compounds, UAs₁-xSex, UPd₂Si₂ or UNi₂Si₂. The above-mentioned systems are made of ferromagnetic layers and the spins from the nearest-neighbor and next-nearest-neighbor layers are coupled by the antiferromagnetic interactions J₁<0 and J₂<0, respectively. Each of these systems exhibits a triple point in which two ordered phases (ferrimagnetic and incommensurate) meet the paramagnetic one, and all undergo the high field phase transition from para- to ferrimagnetic (++-) phase. However, if in UAs₁-xSex the para-ferri phase transition is of the first order as expected from the symmetry reason, in UT₂Si₂ (T=Pd, Ni) this transition seems to be a continuous one, at least in the vicinity of the multicritical point. Within the MFA, the critical character of the finite field para-ferrimagnetic transition at least at one isolated point can be described by the ANNNI model supplemented by an additional, e.g., four-spin interaction. However, in LPRG approximation for the ratio κ = J₂/J₁ around 0.5 there is a critical value of the field for which an isolated critical point also exists in the original ANNNI model. The positive four-spin interaction shifts the critical point towards higher fields and changes the shape of the specific heat curve. In the latter case for the fields small enough, the specific heat exhibits two-peak structure in the paramagnetic phase. |
| format |
Article |
| author |
Sznajd, J. |
| spellingShingle |
Sznajd, J. Linear Perturbation Renormalization Group method for Ising-like spin systems Condensed Matter Physics |
| author_facet |
Sznajd, J. |
| author_sort |
Sznajd, J. |
| title |
Linear Perturbation Renormalization Group method for Ising-like spin systems |
| title_short |
Linear Perturbation Renormalization Group method for Ising-like spin systems |
| title_full |
Linear Perturbation Renormalization Group method for Ising-like spin systems |
| title_fullStr |
Linear Perturbation Renormalization Group method for Ising-like spin systems |
| title_full_unstemmed |
Linear Perturbation Renormalization Group method for Ising-like spin systems |
| title_sort |
linear perturbation renormalization group method for ising-like spin systems |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121079 |
| citation_txt |
Linear Perturbation Renormalization Group method for Ising-like spin systems / J. Sznajd // Condensed Matter Physics. — 2013. — Т. 16, № 1. — С. 13704:1–8. — Бібліогр.: 21 назв. — англ. |
| series |
Condensed Matter Physics |
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AT sznajdj linearperturbationrenormalizationgroupmethodforisinglikespinsystems |
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2023-10-18T20:38:05Z |
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2023-10-18T20:38:05Z |
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