We study effects of competing pairwise higher-order interactions (HOI) with alternating signs and exponentially decreasing intensity on critical behavior of the $XY$ model. It is found that critical properties of such a generalized model can be very different from the standard $XY$ model and can strongly depend on whether the number of HOI terms is odd or even. Inclusion of any odd number of HOI terms results in two consecutive phase transitions to distinct ferromagnetic quasi-long-range order phases. Even number of HOI terms leads to two phase transitions only if the decay of the HOI intensities is relatively slow. Then the high-temperature transition to the ferromagnetic phase is followed by another transition to a peculiar competition-induced canted ferromagnetic phase. In the limit of an infinite number of HOI terms only one phase transition is confirmed, and under the conditions of fierce competition between the even and odd terms the transition temperature can be suppressed practically to zero.We study effects of competing pairwise higher-order interactions (HOI) with alternating signs and exponentially decreasing intensity on critical behavior of the $XY$ model. It is found that critical properties of such a generalized model can be very different from the standard $XY$ model and can strongly depend on whether the number of HOI terms is odd or even. Inclusion of any odd number of HOI terms results in two consecutive phase transitions to distinct ferromagnetic quasi-long-range order phases. Even number of HOI terms leads to two phase transitions only if the decay of the HOI intensities is relatively slow. Then the high-temperature transition to the ferromagnetic phase is followed by another transition to a peculiar competition-induced canted ferromagnetic phase. In the limit of an infinite number of HOI terms only one phase transition is confirmed, and under the conditions of fierce competition between the even and odd terms the transition temperature can be suppressed practically to zero.

arXiv:2112.06791Physical review. EMar 21, 20221 citation

Zeroth-Order Phase Transitions

Виктор Павлович Маслов

Mathematical NotesNov 1, 200441 citations

Properties of phase transitions of higher order

Wolfhard Janke E, Desmond A. Johnston, Ralph Kenna B

There is only limited experimental evidence for the existence in nature of phase transitions of Ehrenfest order greater than two. However, there is no physical reason for their non-existence, and such transitions certainly exist in a number of theoretical models in statistical physics and lattice field theory. Here, higher-order transitions are analysed through the medium of partition function zeros. Results concerning the distributions of zeros are derived as are scaling relations between some of the critical exponents.There is only limited experimental evidence for the existence in nature of phase transitions of Ehrenfest order greater than two. However, there is no physical reason for their non-existence, and such transitions certainly exist in a number of theoretical models in statistical physics and lattice field theory. Here, higher-order transitions are analysed through the medium of partition function zeros. Results concerning the distributions of zeros are derived as are scaling relations between some of the critical exponents.

arXiv:hep-lat/0512022Dec 15, 20050 citations

Properties of phase transitions of higher-order

Ralph Kenna B, Wolfhard Janke E, Desmond A. Johnston

There is only limited experimental evidence for the existence in nature of phase transitions of Ehrenfest order greater than two.However, there is no physical reason for their non-existence, and such transitions certainly exist in a number of theoretical models in statistical physics and lattice field theory.Here, higher-order transitions are analysed through the medium of partition function zeros.Results concerning the distributions of zeros are derived as are scaling relations between some of the critical exponents.There is only limited experimental evidence for the existence in nature of phase transitions of Ehrenfest order greater than two.However, there is no physical reason for their non-existence, and such transitions certainly exist in a number of theoretical models in statistical physics and lattice field theory.Here, higher-order transitions are analysed through the medium of partition function zeros.Results concerning the distributions of zeros are derived as are scaling relations between some of the critical exponents.

Proceedings of XXIIIrd International Symposium on Lattice Field Theory — PoS(LAT2005)Dec 14, 20051 citation

On first order phase transitions

Alain H. Billoire

Nuclear Physics B - Proceedings SupplementsJan 1, 19922 citations

We study effects of competing pairwise higher-order interactions (HOI) with alternating signs and exponentially decreasing intensity on critical behavior of the

XY

model. It is found that critical properties of such a generalized model can be very different from the standard

XY

model and can strongly depend on whether the number of HOI terms is odd or even. Inclusion of any odd number of HOI terms results in two consecutive phase transitions to distinct ferromagnetic quasi-long-range order phases. Even number of HOI terms leads to two phase transitions only if the decay of the HOI intensities is relatively slow. Then the high-temperature transition to the ferromagnetic phase is followed by another transition to a peculiar competition-induced canted ferromagnetic phase. In the limit of an infinite number of HOI terms only one phase transition is confirmed, and under the conditions of fierce competition between the even and odd terms the transition temperature can be suppressed practically to zero.