Violating of the Essam-Fisher and Rushbrooke Relationships at Low Temperatures

Udodov, V. N.

doi:10.4236/wjcmp.2015.52008

Cited by 4 publications

(1 citation statement)

References 10 publications

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“…Существует строгое термодинамиче-ское доказательство двух неравенств, частным случа-ем которых являются предыдущие равенства. Это не-равенство Рашбрука [7] 2 2 α β γ + + ≥ и Гриффитса [8] (1 ) 2 α β δ + + ≥ . В теории однородного самосогла-сованного поля Гиббса -Вейса Ландау соотношения подобия выполняются, в рамках данных теорий значения индексов (для ФП 2-го рода): α=0, β=1/2, γ=1, δ=3 [6].…”

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Fulfillment of Dynamic and Static Scaling Hypotheses for an Ising Nanomagnet

Dzyuba¹,

Udodov²

2017

izvasu

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Представлены результаты компьютерного мо-делирования обобщенной модели Изинга квазиод-номерного наномагнетика при фазовом переходе антиферромагнетик -ферромагнетик с периодиче-скими граничными условиями методом Монте-Карло. Используя значения критической температуры, а так-же значения критических индексов, авторы проверили соотношение динамического скейлинга изинговского наномагнетика, а именно выполнения соотношения Y = v* z и статического скейлинга dv = 2 -α. Для ли-нейной системы (кластера) конечного размера по-строены температурные зависимости кинетического критического индекса Y(T) и произведения динамиче-ского критического индекса на индекс корреляцион-ной длины v* z(T). Описано влияние энергии взаимо-действия вторых, третьих соседей, четырехчастичного взаимодействия на выполнение гипотез динамическо-го и статического скейлинга. Найдены параметры, при которых соотношение динамического скейлинга в пределах погрешности выполняется вблизи крити-ческой области. Показано, что гипотеза статического скейлинга в рамках модели одномерного изинговско-го магнетика вблизи критической области нарушается для средних значений индексов при любом типе вза-имодействия, однако в пределах погрешности расче-та при некоторых температурах соотношение v + α = 2 выполняется. Полученные результаты сопоставлены со значениями для модели Изинга с граничными ус-ловиями «оборванные концы». The influence of interaction energy of the second, third neighbors, and four-particle interaction on the fulfillment of dynamic and static scaling hypotheses is described. Parameters are found for the dynamic scaling ratio near the critical region to be within the errors. It is shown that the static scaling hypothesis within the framework of the one-dimensional Ising magnet model near the critical region is violated for any type of interaction. However, the relation v + α = 2 is satisfied within the errors for some temperatures. The obtained results are compared with the values for the Ising model with the «dangling ends» boundary conditions.

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Fulfillment of Dynamic and Static Scaling Hypotheses for an Ising Nanomagnet

Dzyuba¹,

Udodov²

2017

izvasu

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The epsilon expansion near absolute zero

Udodov

2020

J. Phys.: Conf. Ser.

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Epsilon expansion is an important part of the renormalization group approach; it allows substantiating the scaling paradigm and is used in the modern theory of critical phenomena. It is shown that at a critical temperature equal to zero, the expression for the critical heat capacity exponent already in the first order in epsilon d − = 4 – (d – is the dimension of space) changes its form. This, however, does not indicate a violation of the scaling approach, although the classical Essam-Fisher equation also changes, as does the Rushbrook inequality. The generalized Essam-Fisher interpolation equality and the generalized Rushbrook inequality are given, which are valid for any value of the critical temperature, in particular, for the critical temperature equal to zero. The generalized relations are consistent with the renormalization-group approach, - expansion and scaling paradigm. The fluctuations are considered to be classical (thermodynamic), the conditions are determined when this takes place.

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Spherical model and quantum phase transitions

Udodov

2021

J. Phys.: Conf. Ser.

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The spherical Berlin-Katz model is considered in the framework of the epsilon expansion in one-dimensional and two-dimensional space. For the two-dimensional and threedimensional cases in this model, an exact solution was previously obtained in the presence of a field, and for the two-dimensional case the critical temperature is zero, that is, a “quantum” phase transition is observed. On the other hand, the epsilon expansion of critical exponents with an arbitrary number of order parameter components is known. This approach is consistent with the scaling paradigm. Some critical exponents are found for the spherical model in one-and twodimensional space in accordance with the generalized scaling paradigm and the ideas of quantum phase transitions. A new formula is proposed for the critical heat capacity exponent, which depends on the dynamic index z, at a critical temperature equal to zero. An expression is proposed for the order of phase transition with a change in temperature (developing the approach of R. Baxter), which also depends on the z index. An interpolation formula is presented for the effective dimension of space, which is valid for both a positive critical temperature and a critical temperature equal to zero. This formula is general. Transitions with a change in the field in a spherical model at absolute zero are also considered.

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Violating of the Essam-Fisher and Rushbrooke Relationships at Low Temperatures

Cited by 4 publications

References 10 publications

Fulfillment of Dynamic and Static Scaling Hypotheses for an Ising Nanomagnet

Fulfillment of Dynamic and Static Scaling Hypotheses for an Ising Nanomagnet

The epsilon expansion near absolute zero

Spherical model and quantum phase transitions

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