[ALPS-users] How to count dimension of graph defined in Lattice xml library

[Matthias Troyer]

Arbitrary graphs don’t have a “dimension”. Only lattices do.

> On 9 Nov 2017, at 14:12, Sun Rongyang <sun-rongyang at outlook.com> wrote:
> 
> Dear all,
> 
> The definition method of a lattice in ALPS is delicate. But I meet a problem about dimension counting of a pure graph. On the one hand, I define an pure anisotropic graph as:
> 
> *************************************************************************************************
> <GRAPH name="anisotropic open ladder graph test">
>     <!-- type="0" means horizontal; type="1" means vertical -->
>     <EDGE tyep="0" source="1" target="2"/>
>     <EDGE tyep="0" source="2" target="3"/>
>     <EDGE tyep="0" source="3" target="4"/>
>     <EDGE tyep="0" source="4" target="5"/>
>     <EDGE tyep="0" source="6" target="7"/>
>     <EDGE tyep="0" source="7" target="8"/>
>     <EDGE tyep="0" source="8" target="9"/>
>     <EDGE tyep="0" source="9" target="10"/>
>     <EDGE tyep="1" source="1" target="6"/>
>     <EDGE tyep="1" source="2" target="7"/>
>     <EDGE tyep="1" source="3" target="8"/>
>     <EDGE tyep="1" source="4" target="9"/>
>     <EDGE tyep="1" source="5" target="10"/>
> </GRAPH>
> *************************************************************************************************
> On the other hand, I use the default LATTICEGRAPH "open ladder", I copy here:
> 
> *************************************************************************************************
> <LATTICE name="square lattice" dimension="2">
>   <PARAMETER name="a" default="1"/>
>   <BASIS><VECTOR>a 0</VECTOR><VECTOR>0 a</VECTOR></BASIS>
>   <RECIPROCALBASIS><VECTOR>2*pi/a 0</VECTOR><VECTOR>0 2*pi/a</VECTOR></RECIPROCALBASIS>
> </LATTICE>
> 
> <UNITCELL name="anisotropic2d" dimension="2">
>   <VERTEX/>
>   <EDGE type="0"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="1 0"/></EDGE>
>   <EDGE type="1"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="0 1"/></EDGE>
> </UNITCELL>
> 
> <LATTICEGRAPH name = "open ladder" vt_name="OpenLadderLattice">
>   <FINITELATTICE>
>     <LATTICE ref="square lattice"/>
>     <PARAMETER name="W" default="2"/>
>     <EXTENT dimension="1" size="L"/>
>     <EXTENT dimension="2" size="W"/>
>     <BOUNDARY dimension="1" type="open"/>
>     <BOUNDARY dimension="2" type="open"/>
>   </FINITELATTICE>
>   <UNITCELL ref="anisotropic2d"/>
> </LATTICEGRAPH>
> *************************************************************************************************
> with parameters L=2, W=5. Will they be treated as the same in ALPS? Or the graph equals as L=5,W=2 open ladder?
> 
> Thanks a lot!
> 
> Best regards,
> Rongyang Sun
>  
> 
> 
> 
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