Ladder ising spin configurations. I. Heat capacity

Abstract

We consider a ladder Ising spin model (with two coupled Ising spin chains), characterized by two couplings (interchain and intrachain couplings), to study in detail, in an analytical way, its thermal behaviour and particularly the variation of the specific heat versus temperature, the ratio of interaction constants, and the magnetic field. It is interesting that when the competition betwecn interchain and intrachain interactions is strong the specific heat exhibits a double peak and when the compctition is not, so strong the specific heat has a single peak. Further, without entering into details, we give, in a numerical way, some similar results for more complicated ladder configurations (with more than two linear king chains). The spin-; ladders or systems of spin chains may be realized in nature by vanadyl pyrophosphate ((VO),PzO7) or similar materials. All these intermediate systems are today important to gain further insight into the physics of one-dimensional spin chains and two-dimensional high-TL spin systems, both of which have shown interesting and unusual magnetic and superconducting properties. It is plausible that experimental and theoretical studies of ladders may lead to other interesting physical phenomena.

Double-peak specific heat anomaly and correlations in the Bose-Hubbard model

“…Other examples include heavyfermion compounds [11,12], bosonic superfluids in spindimer networks [13], CO 2 N 2 plasma [14], lipid bilayers containing colesterol [15], as wells as mixtures of liquid crystal and nanoparticles [16]. In a theoretical framework, the anomaly was verified for spin models with antiferromagnetic Heisenberg interactions [17][18][19][20][21][22], Ising pyrochlore magnets using Monte Carlo simulations [23,24], Ising models [25][26][27][28] in distinct geometries, and quantum ferrimagnets [29].…”

A pseudo-two-dimensional Ising model of ferroelectrics

“…We denote by J x the nearest-neighbour interaction along the long axis of the ladder, by J z the nearest-neighbour interaction across the rungs of the ladder (J x and J z are the intraladder couplings) and by J y the inter-ladder interaction between two nearest-neighbour spins (or dipoles) (figure 1). The Hamiltonian of this model for nearest-neighbour interactions is (1) (i, j )S (1) (i + 1, j) + S (2) (i, j )S (2)…”

“…where E is the electric field and S (1) (i, j ) or S (2) (i, j ) = ±1 at site (i, j ) of plane ( 1) or (2), respectively. We will also consider periodic boundary conditions in the x and y axis directions.…”

“…In [1,2] we considered Ising spin ladders to study in detail the behaviour of different thermodynamic properties related to different values of temperature, the ratio of interaction constants and the magnetic field. These systems, like the other intermediate systems, can help to provide further insight into the physics of 1D spin chains and 2D high-T c spin systems, both of which have shown interesting and unusual magnetic and superconducting properties (see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and references therein).…”

“…These systems, like the other intermediate systems, can help to provide further insight into the physics of 1D spin chains and 2D high-T c spin systems, both of which have shown interesting and unusual magnetic and superconducting properties (see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and references therein). Thus, the orthorhombic compound vanadyl pyrophosphate (VO) 2 P 2 O 7 clearly shows a ladder configuration of spin- 1 2 V 4+ ions in its crystal lattice. Also, some years ago, many theories based upon the pseudo-onedimensional (1D) Ising model were applied to explain the thermodynamic properties of the 1D ferroelectrics such as CsH 2 PO 4 (CDP), PbHPO 4 (PMP) and their deuterated analogues d-CDP and d-PMP ( [18][19][20][21][22][23][24] and references therein).…”